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    <link:label id="lab_fbc_RealPropertyCollateralMember_d0eef314-21e5-4473-9723-977b77b55cc2_terseLabel_en-US" xlink:label="lab_fbc_RealPropertyCollateralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral Type</link:label>
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    <link:label id="lab_fbc_RealPropertyCollateralMember_documentation_en-US" xlink:label="lab_fbc_RealPropertyCollateralMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Property Collateral</link:label>
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    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanPlanAssetsTargetAllocationPercentage_5a20f921-d596-4dfd-b529-ab3f630403ff_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanPlanAssetsTargetAllocationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Allocation Parameters by Asset Class</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanPlanAssetsTargetAllocationPercentage_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanPlanAssetsTargetAllocationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Plan Assets, Target Allocation, Percentage</link:label>
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    <link:label id="lab_fbc_StrikePriceOfWarrants_841fb174-5499-44b7-a918-ad052cdb63b7_terseLabel_en-US" xlink:label="lab_fbc_StrikePriceOfWarrants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Strike price (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesFloatingRateAbstract_223403af-9320-4386-98ce-8a3bfa885289_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesFloatingRateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contractual Maturity</link:label>
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    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_bac28f8b-a01a-4ab1-8c02-b9b6f5d44f94_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting and Reporting Developments And Standards adopted in 2025 And Significant Standards Issued but Not Yet Adopted</link:label>
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    <link:label id="lab_fbc_InterestRateSwapsandSwaptionsMember_8ce8d30f-4b43-4d81-9ad0-dea8b21fed2b_terseLabel_en-US" xlink:label="lab_fbc_InterestRateSwapsandSwaptionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swaps and swaptions</link:label>
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    <link:label id="lab_fbc_InterestRateSwapsandSwaptionsMember_label_en-US" xlink:label="lab_fbc_InterestRateSwapsandSwaptionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swaps and Swaptions [Member]</link:label>
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    <link:label id="lab_us-gaap_SharesSubjectToMandatoryRedemptionSettlementTermsAmount_c892fbf2-7fcc-4ac7-9f7f-cd75fe6d0af2_terseLabel_en-US" xlink:label="lab_us-gaap_SharesSubjectToMandatoryRedemptionSettlementTermsAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital Securities Amount Outstanding</link:label>
    <link:label id="lab_us-gaap_SharesSubjectToMandatoryRedemptionSettlementTermsAmount_label_en-US" xlink:label="lab_us-gaap_SharesSubjectToMandatoryRedemptionSettlementTermsAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments Subject to Mandatory Redemption, Settlement Terms, Share Value, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesSubjectToMandatoryRedemptionSettlementTermsAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharesSubjectToMandatoryRedemptionSettlementTermsAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesSubjectToMandatoryRedemptionSettlementTermsAmount" xlink:to="lab_us-gaap_SharesSubjectToMandatoryRedemptionSettlementTermsAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EquityInstrumentFDICAppreciationIssued_4094831f-7876-4154-b7a1-147943645472_terseLabel_en-US" xlink:label="lab_fbc_EquityInstrumentFDICAppreciationIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of FDIC Equity appreciation instrument</link:label>
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    <link:label id="lab_fbc_EquityInstrumentFDICAppreciationIssued_documentation_en-US" xlink:label="lab_fbc_EquityInstrumentFDICAppreciationIssued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Instrument, FDIC Appreciation, Issued</link:label>
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    <link:label id="lab_fbc_FederalHomeLoanBankAdvanceMaturityYearSeven_14eb2835-5515-49c0-af92-fd1c6d89c9d9_terseLabel_en-US" xlink:label="lab_fbc_FederalHomeLoanBankAdvanceMaturityYearSeven" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2032</link:label>
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    <link:label id="lab_fbc_FederalHomeLoanBankAdvanceMaturityYearSeven_documentation_en-US" xlink:label="lab_fbc_FederalHomeLoanBankAdvanceMaturityYearSeven" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advance, Maturity, Year Seven</link:label>
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    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_b60b1eb0-abc0-42d6-bebe-2421d3344b04_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Carrying Amount and Estimated Fair Value of Financial Instruments</link:label>
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    <link:label id="lab_fbc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice_5021a417-3fd5-490d-ac8b-e3ed26ce048a_terseLabel_en-US" xlink:label="lab_fbc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vested (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_AffordableHousingProjectInvestmentWriteDownAmount_a58cc4a5-9c5c-4efb-b1c9-fb9d9b0e08f4_terseLabel_en-US" xlink:label="lab_us-gaap_AffordableHousingProjectInvestmentWriteDownAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Affordable housing tax credit write down</link:label>
    <link:label id="lab_us-gaap_AffordableHousingProjectInvestmentWriteDownAmount_label_en-US" xlink:label="lab_us-gaap_AffordableHousingProjectInvestmentWriteDownAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Program, Proportional Amortization Method, Elected, Impairment Loss</link:label>
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    <link:label id="lab_us-gaap_GuaranteeObligationsMaximumExposure_a505c7be-fddb-4e57-b3ff-c78bd7beaf11_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsMaximumExposure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stand-by letters of credit</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesMember_b9332bd5-fd8f-492f-8166-b7080f0bdab1_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesMember_139b90ed-b876-4365-ae27-df909da387b3_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other debt securities available-for-sale:</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract_9579b928-b94c-43dc-b5f8-5157e1587054_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive gain (loss), net of tax:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablePortfolioSegmentDomain"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery_94ece281-3d88-4711-9ca1-522d3b409914_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRecovery" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recoveries</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanPlanAssetsCategoryTable_55a0d597-0c24-4b14-836a-b75c6dc1dd97_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanPlanAssetsCategoryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Plan Assets, Category [Table]</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansBeforeTax_344db70f-c029-4492-8167-4a9a165b79ea_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansBeforeTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total recognized in other comprehensive income (loss) for the year (pre-tax)</link:label>
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    <link:label id="lab_us-gaap_BankingRegulationCommonEquityTierOneRiskBasedCapitalRatioCapitalAdequacyMinimum_e3039a28-e470-4b27-be40-563d7b6ebd59_terseLabel_en-US" xlink:label="lab_us-gaap_BankingRegulationCommonEquityTierOneRiskBasedCapitalRatioCapitalAdequacyMinimum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum for capital adequacy, ratio</link:label>
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    <link:label id="lab_us-gaap_DerivativeAssetNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Notional Amount</link:label>
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    <link:label id="lab_us-gaap_EmployeeStockOptionMember_1c626e33-61eb-43c5-93e4-55add543460f_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_70f88c0a-9bab-47e2-bd24-4659a4418bd5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_c0cffd52-b418-45ec-b585-b8d5c9bd6aa6_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Due from Banks, Interest Earning Deposits, Cash Equivalents and Restricted Cash</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
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    <link:label id="lab_fbc_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter_c4b2f6cc-f141-4772-ba4f-59767273aa48_terseLabel_en-US" xlink:label="lab_fbc_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2031 and beyond</link:label>
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    <link:label id="lab_fbc_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter_documentation_en-US" xlink:label="lab_fbc_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Five And Thereafter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter" xlink:href="fbc-20251231.xsd#fbc_FiniteLivedIntangibleAssetExpectedAmortizationYearFiveAndThereafter"/>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract_019b92ef-4df9-73ce-b84a-b43914350692_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent</link:label>
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    <link:label id="lab_us-gaap_ConsumerLoanMember_3a962441-f5c9-4e68-9195-7889501cdb8f_terseLabel_en-US" xlink:label="lab_us-gaap_ConsumerLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Consumer</link:label>
    <link:label id="lab_us-gaap_ConsumerLoanMember_label_en-US" xlink:label="lab_us-gaap_ConsumerLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consumer Loan [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsumerLoanMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsumerLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsumerLoanMember" xlink:to="lab_us-gaap_ConsumerLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax_ea5e8dcf-577b-49cd-8484-05fd2d9317e4_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gain (loss) on cash flow hedges</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), before Reclassification, Tax</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquity_dc952ba5-7eca-4532-8390-425863e7f520_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders&#8217; equity</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
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    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_25b938cf-0742-4a1e-a3ec-b9ba030c04e3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_a57449ae-ffca-4fd2-b988-d7eb675539be_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale Securities [Table]</link:label>
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    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
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    <link:label id="lab_stpr_NY_019b92f3-5b90-7530-ac78-dcb14bc7165f_terseLabel_en-US" xlink:label="lab_stpr_NY" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New York State</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_8fa77759-9526-44b6-aba3-ae5aa1b7da06_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Premises and Equipment and Estimated Useful Lives</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_0b86fb6b-7c0b-4612-a00d-7bde4a3def14_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Assets:</link:label>
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    <link:label id="lab_fbc_OtherLoansMember_117ba31a-4f08-4f9a-bf06-308ceb865baa_terseLabel_en-US" xlink:label="lab_fbc_OtherLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_d99e8a62-2266-4edb-82bb-83d9d04e8cb9_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_16ce8968-db9e-4c79-9db9-a9974fb6142f_totalLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition_37a9e51b-f327-43fc-ac31-7eafe8796461_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentLineItems_75f8e1de-ccfc-4d80-b03e-9960814e840f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument</link:label>
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    <link:label id="lab_us-gaap_OtherAssetsMember_36f93b21-cedb-4f4b-8e49-c385fdee5d5b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets [Member]</link:label>
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    <link:label id="lab_us-gaap_TemporaryEquityLineItems_6c9682a0-6bc0-4e19-9393-16638ba6bbec_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary Equity [Line Items]</link:label>
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    <link:label id="lab_us-gaap_TierOneLeverageCapitalToAverageAssets_cc07e12f-9cc8-4765-bd5c-7a6af19724a7_terseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalToAverageAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total capital, ratio</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentTable_09f2b0fd-afa8-4376-be2c-5997139ff80c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectFinancingLeaseLeaseReceivable_9e9f630b-38ac-4a92-b6a8-36d6d150f9cb_terseLabel_en-US" xlink:label="lab_us-gaap_DirectFinancingLeaseLeaseReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease payments receivable</link:label>
    <link:label id="lab_us-gaap_DirectFinancingLeaseLeaseReceivable_label_en-US" xlink:label="lab_us-gaap_DirectFinancingLeaseLeaseReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Financing Lease, Lease Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectFinancingLeaseLeaseReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DirectFinancingLeaseLeaseReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectFinancingLeaseLeaseReceivable" xlink:to="lab_us-gaap_DirectFinancingLeaseLeaseReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseOperating_ffcbbe1f-247d-42d8-8195-468d09be02b6_totalLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_0d334ae5-033c-43da-a391-16790c8b3c86_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense - Borrowed funds</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseOperating" xlink:to="lab_us-gaap_InterestExpenseOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_BifurcatedOptionNotesUnitSecuritiesMember_b510d0f9-13d5-45d0-850a-d8c873db1794_terseLabel_en-US" xlink:label="lab_fbc_BifurcatedOptionNotesUnitSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bifurcated Option Notes Unit Securities</link:label>
    <link:label id="lab_fbc_BifurcatedOptionNotesUnitSecuritiesMember_label_en-US" xlink:label="lab_fbc_BifurcatedOptionNotesUnitSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bifurcated Option Notes Unit Securities [Member]</link:label>
    <link:label id="lab_fbc_BifurcatedOptionNotesUnitSecuritiesMember_documentation_en-US" xlink:label="lab_fbc_BifurcatedOptionNotesUnitSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Bifurcated option notes unit securities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_BifurcatedOptionNotesUnitSecuritiesMember" xlink:href="fbc-20251231.xsd#fbc_BifurcatedOptionNotesUnitSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_BifurcatedOptionNotesUnitSecuritiesMember" xlink:to="lab_fbc_BifurcatedOptionNotesUnitSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_OperatingLeaseAssetsAndLiabilitiesLesseeAbstract_3899c7cb-db1a-4199-929b-9cd08f2d1551_terseLabel_en-US" xlink:label="lab_fbc_OperatingLeaseAssetsAndLiabilitiesLesseeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Leases:</link:label>
    <link:label id="lab_fbc_OperatingLeaseAssetsAndLiabilitiesLesseeAbstract_label_en-US" xlink:label="lab_fbc_OperatingLeaseAssetsAndLiabilitiesLesseeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Assets And Liabilities, Lessee [Abstract]</link:label>
    <link:label id="lab_fbc_OperatingLeaseAssetsAndLiabilitiesLesseeAbstract_documentation_en-US" xlink:label="lab_fbc_OperatingLeaseAssetsAndLiabilitiesLesseeAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating Lease, Assets And Liabilities, Lessee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_OperatingLeaseAssetsAndLiabilitiesLesseeAbstract" xlink:href="fbc-20251231.xsd#fbc_OperatingLeaseAssetsAndLiabilitiesLesseeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_OperatingLeaseAssetsAndLiabilitiesLesseeAbstract" xlink:to="lab_fbc_OperatingLeaseAssetsAndLiabilitiesLesseeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_TX_019b92f5-13a6-7141-b323-d74301015392_terseLabel_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Texas</link:label>
    <link:label id="lab_stpr_TX_label_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">TEXAS</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_TX" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_TX"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_TX" xlink:to="lab_stpr_TX" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_7ac6fcb7-d7d4-4083-83de-82adfbc83e65_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease_275b5b7d-92e1-45c0-ab44-b1a8242366f0_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation increase percentage</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Assumptions Used Calculating Net Periodic Benefit Cost, Rate of Compensation Increase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease" xlink:to="lab_us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostRateOfCompensationIncrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesAuthorized_aa998356-ec8a-44f1-8635-d24e648c91f2_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncumulative convertible preferred stock (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesAuthorized_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquitySharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesAuthorized" xlink:to="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesFairValueLineItems_a8eda0fa-f260-4a4b-b324-d1faa3121649_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives, Fair Value [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativesFairValueLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativesFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Fair Value [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesFairValueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativesFairValueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesFairValueLineItems" xlink:to="lab_us-gaap_DerivativesFairValueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock_0dfd04ba-313c-46a2-89a1-8f7660e3af92_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Differences between Aggregate Fair Value and Aggregate Remaining Contractual Principal Balance Outstanding - Fair Value Option</link:label>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Option, Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_ddbeba12-e971-419f-afb8-4a2f988982e6_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Accrual Loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_ServicingAssetAtFairValueNetTransactionCosts_bccb17c4-f370-43a8-8ded-133662a7d680_terseLabel_en-US" xlink:label="lab_fbc_ServicingAssetAtFairValueNetTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net transaction costs</link:label>
    <link:label id="lab_fbc_ServicingAssetAtFairValueNetTransactionCosts_label_en-US" xlink:label="lab_fbc_ServicingAssetAtFairValueNetTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset At Fair Value, Net Transaction Costs</link:label>
    <link:label id="lab_fbc_ServicingAssetAtFairValueNetTransactionCosts_documentation_en-US" xlink:label="lab_fbc_ServicingAssetAtFairValueNetTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The total amount of net transaction costs earned on loans serviced and subserviced for others during the period for which results of operations are presented.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_ServicingAssetAtFairValueNetTransactionCosts" xlink:href="fbc-20251231.xsd#fbc_ServicingAssetAtFairValueNetTransactionCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_ServicingAssetAtFairValueNetTransactionCosts" xlink:to="lab_fbc_ServicingAssetAtFairValueNetTransactionCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss_4d46301f-0ff9-43a7-b452-3e486f2c1596_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_e8e1f796-e07b-4bd4-9408-ba5c8129bb89_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_97a58759-3c6f-4a46-8e39-9cd45e2ef9c4_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_label_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingRelationshipDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HedgingRelationshipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingRelationshipDomain" xlink:to="lab_us-gaap_HedgingRelationshipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears_44c742df-3935-42ef-91d9-07608893e6b5_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears" xlink:to="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThreeYears" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ParentCompanyMember_843fbe49-1631-401b-a489-624b26892c23_terseLabel_en-US" xlink:label="lab_srt_ParentCompanyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Parent company</link:label>
    <link:label id="lab_srt_ParentCompanyMember_label_en-US" xlink:label="lab_srt_ParentCompanyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Parent Company [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ParentCompanyMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ParentCompanyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ParentCompanyMember" xlink:to="lab_srt_ParentCompanyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueOtherChangesInFairValue_4ae55696-fbaf-42b7-abdc-b7c705b3fa30_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueOtherChangesInFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Decrease in MSR fair value due to pay-offs, pay-downs, run-off, model changes and other</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueOtherChangesInFairValue_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueOtherChangesInFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Fair Value, Other Changes in Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtFairValueOtherChangesInFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAtFairValueOtherChangesInFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtFairValueOtherChangesInFairValue" xlink:to="lab_us-gaap_ServicingAssetAtFairValueOtherChangesInFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_019b9328-4a18-7174-94a3-167666690129_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plans And Stock-Based Compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:to="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_5b38b9ba-ed98-4ae9-ab64-4e72f7fef9b4_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_d5777721-cd0b-4505-84f8-60611c64f1e9_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_5a9919f5-16aa-498c-999a-3b7160560b07_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Assets Acquired and Liabilities Assumed</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationsPolicy" xlink:to="lab_us-gaap_BusinessCombinationsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseLongTermDebt_37216ef4-e27e-47a9-8978-d368f028a764_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowed funds</link:label>
    <link:label id="lab_us-gaap_InterestExpenseLongTermDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseLongTermDebt" xlink:to="lab_us-gaap_InterestExpenseLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_52628b23-69f6-44c6-8505-d8142d86840c_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_feb1456f-d5d4-437a-b25e-93b56dbd873a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_FlagstarStatutoryTrustVIIIMember_dd26d7be-0edc-4a97-9d58-251387c34e66_terseLabel_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustVIIIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust VIII</link:label>
    <link:label id="lab_fbc_FlagstarStatutoryTrustVIIIMember_label_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustVIIIMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust VIII [Member]</link:label>
    <link:label id="lab_fbc_FlagstarStatutoryTrustVIIIMember_documentation_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustVIIIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust VIII</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FlagstarStatutoryTrustVIIIMember" xlink:href="fbc-20251231.xsd#fbc_FlagstarStatutoryTrustVIIIMember"/>
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    <link:label id="lab_fbc_OfficersAndDirectorsMember_bbfd5310-5e5b-4f0b-a3f8-f23f7cb27bc6_terseLabel_en-US" xlink:label="lab_fbc_OfficersAndDirectorsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Officers And Directors</link:label>
    <link:label id="lab_fbc_OfficersAndDirectorsMember_label_en-US" xlink:label="lab_fbc_OfficersAndDirectorsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Officers And Directors [Member]</link:label>
    <link:label id="lab_fbc_OfficersAndDirectorsMember_documentation_en-US" xlink:label="lab_fbc_OfficersAndDirectorsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Officers And Directors</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_OfficersAndDirectorsMember" xlink:href="fbc-20251231.xsd#fbc_OfficersAndDirectorsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_OfficersAndDirectorsMember" xlink:to="lab_fbc_OfficersAndDirectorsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsDisclosureTextBlock_b0206c54-698e-4edc-a98b-96833b42590c_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Assets</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt_31dedec7-9297-47e4-85d1-3bac4156d219_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in short-term advances</link:label>
    <link:label id="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from (Repayments of) Short-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromRepaymentsOfShortTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromRepaymentsOfShortTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromRepaymentsOfShortTermDebt" xlink:to="lab_us-gaap_ProceedsFromRepaymentsOfShortTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_6a411a79-6225-469d-8906-e2cb372abe69_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationDomain" xlink:to="lab_us-gaap_IncomeStatementLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_60511275-b105-490e-b0a3-7434d6eb9564_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Stock Units (RSUs)</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units (RSUs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockUnitsRSUMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:to="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TimeDepositsAtOrAboveFDICInsuranceLimit_9aaa9a46-827d-46e6-8280-4d7b4f90b6d7_terseLabel_en-US" xlink:label="lab_us-gaap_TimeDepositsAtOrAboveFDICInsuranceLimit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate amount of time deposit accounts</link:label>
    <link:label id="lab_us-gaap_TimeDepositsAtOrAboveFDICInsuranceLimit_label_en-US" xlink:label="lab_us-gaap_TimeDepositsAtOrAboveFDICInsuranceLimit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time Deposits, at or Above FDIC Insurance Limit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TimeDepositsAtOrAboveFDICInsuranceLimit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositsAtOrAboveFDICInsuranceLimit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TimeDepositsAtOrAboveFDICInsuranceLimit" xlink:to="lab_us-gaap_TimeDepositsAtOrAboveFDICInsuranceLimit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock_a46615d4-ef48-40fe-9af6-aa73a9b9cb03_terseLabel_en-US" xlink:label="lab_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Credit Losses on Loans and Leases and Unfunded Commitments</link:label>
    <link:label id="lab_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Loss, Financial Instrument [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditLossFinancialInstrumentPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xlink:to="lab_us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseShortTermBorrowings_019b8f3b-5561-7e3d-a1d9-aeb045275e70_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseShortTermBorrowings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense on short-term borrowings</link:label>
    <link:label id="lab_us-gaap_InterestExpenseShortTermBorrowings_label_en-US" xlink:label="lab_us-gaap_InterestExpenseShortTermBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Short-Term Borrowings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseShortTermBorrowings" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseShortTermBorrowings"/>
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    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_79b0464b-d0a6-4079-ba19-f70bedc1ccc5_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase Price consideration</link:label>
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    <link:label id="lab_dei_EntityEmergingGrowthCompany_0371250b-a7d1-467d-82ca-8464f0df6fac_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
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    <link:label id="lab_us-gaap_CommonEquityTierOneCapitalRatio_11751846-005e-4423-883e-600368b943ed_terseLabel_en-US" xlink:label="lab_us-gaap_CommonEquityTierOneCapitalRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total capital, ratio</link:label>
    <link:label id="lab_us-gaap_CommonEquityTierOneCapitalRatio_label_en-US" xlink:label="lab_us-gaap_CommonEquityTierOneCapitalRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Common Equity Tier 1 Risk-Based Capital Ratio, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonEquityTierOneCapitalRatio" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonEquityTierOneCapitalRatio"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanAccumulatedOtherComprehensiveIncomeBeforeTax_4fd597aa-c56d-4712-bd2b-b91ea58cc4f4_totalLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAccumulatedOtherComprehensiveIncomeBeforeTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total accumulated other comprehensive loss (pre-tax)</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanAccumulatedOtherComprehensiveIncomeBeforeTax_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAccumulatedOtherComprehensiveIncomeBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Accumulated Other Comprehensive (Income) Loss, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanAccumulatedOtherComprehensiveIncomeBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanAccumulatedOtherComprehensiveIncomeBeforeTax"/>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesTextBlock_601b15c3-023e-4b91-a1fc-88af08843910_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Unrealized Loss Positions on Investment Securities Held-to-Maturity</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesTextBlock_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesTextBlock"/>
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    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimCash_c2f79db2-b9db-4b13-ade6-7baf98eb03aa_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Collateral Pledged (Received)</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimCash_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Cash Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeCollateralRightToReclaimCash"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_f3166735-de89-4f88-8199-8d4ac73ce98b_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Outstanding, beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber"/>
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    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
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    <link:label id="lab_us-gaap_UnfundedLoanCommitmentMember_161e0f1e-f51d-452d-98f8-c23eb01c954a_terseLabel_en-US" xlink:label="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total loan commitments</link:label>
    <link:label id="lab_us-gaap_UnfundedLoanCommitmentMember_label_en-US" xlink:label="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unfunded Loan Commitment [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnfundedLoanCommitmentMember" xlink:to="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsNextTwelveMonths_808fdce5-1884-44aa-8f44-89ffad1d0186_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsNextTwelveMonths"/>
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    <link:label id="lab_us-gaap_InterestExpenseTimeDeposits_f60508ab-e2db-4700-9a84-6c704b489d78_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseTimeDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Certificates of deposit</link:label>
    <link:label id="lab_us-gaap_InterestExpenseTimeDeposits_label_en-US" xlink:label="lab_us-gaap_InterestExpenseTimeDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Time Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseTimeDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseTimeDeposits"/>
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    <link:label id="lab_us-gaap_InvestmentProportionalAmortizationMethodElectedStatementOfFinancialPositionExtensibleEnumeration_a2b06e61-4aac-48c3-94e2-1c0f8cde5b35_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentProportionalAmortizationMethodElectedStatementOfFinancialPositionExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Proportional Amortization Method, Elected, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_InvestmentProportionalAmortizationMethodElectedStatementOfFinancialPositionExtensibleEnumeration_label_en-US" xlink:label="lab_us-gaap_InvestmentProportionalAmortizationMethodElectedStatementOfFinancialPositionExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Proportional Amortization Method, Elected, Statement of Financial Position [Extensible Enumeration]</link:label>
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    <link:label id="lab_us-gaap_NoninterestIncome_5477495b-9343-46bc-be7e-66cf22bc7066_totalLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncome" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total non-interest income</link:label>
    <link:label id="lab_us-gaap_NoninterestIncome_label_en-US" xlink:label="lab_us-gaap_NoninterestIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestIncome"/>
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    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_a48a6e2c-4892-4069-a1c7-7e3dac413e3a_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
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    <link:label id="lab_us-gaap_GainLossOnSalesOfLoansNet_8d09aa9b-0a59-4aef-9eb2-8f25c0f7250c_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSalesOfLoansNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gain on loan sales and securitizations</link:label>
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    <link:label id="lab_us-gaap_InterestRateSwaptionMember_b34dc587-821a-4cca-8678-600bce7fc85a_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateSwaptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swaps</link:label>
    <link:label id="lab_us-gaap_InterestRateSwaptionMember_label_en-US" xlink:label="lab_us-gaap_InterestRateSwaptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swaption [Member]</link:label>
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    <link:label id="lab_us-gaap_OtherAssetsFairValueDisclosure_c7d8cafa-80db-45e4-9a5d-d081a1d93fdb_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_OtherAssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Fair Value Disclosure</link:label>
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    <link:label id="lab_us-gaap_NoninterestExpenseAbstract_938a2317-d22e-4ade-bcb1-935c4c16aa15_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NON-INTEREST EXPENSE:</link:label>
    <link:label id="lab_us-gaap_NoninterestExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_NoninterestExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Expense [Abstract]</link:label>
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    <link:label id="lab_us-gaap_CashAndDueFromBanks_019be967-86c5-78be-a29c-f296415d5976_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndDueFromBanks" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and due from banks</link:label>
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    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
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    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentEquityAppreciationInstrument_1d847601-3fc5-44d6-a066-7e3041211b3d_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentEquityAppreciationInstrument" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FDIC Equity Appreciation Instrument</link:label>
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    <link:label id="lab_us-gaap_IntangibleAssetsFiniteLivedPolicy_a53c1771-bea4-4532-bff7-88024d666af5_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsFiniteLivedPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Assets</link:label>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_ac690c5d-0309-45c7-be8f-f0f85de41fde_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableModifiedWeightedAverageInterestRateDecreaseFromModification_06068b0b-d36b-45d1-8ccd-63fd7cf3e60b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableModifiedWeightedAverageInterestRateDecreaseFromModification" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-Average Contractual Interest Rate</link:label>
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    <link:label id="lab_dei_EntityAddressPostalZipCode_0b74dc95-4f08-4221-81f6-33f726fa9b4f_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
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    <link:label id="lab_us-gaap_InterestBearingDomesticDepositCertificatesOfDeposits_e7e6cb14-b45a-4f34-b98e-cf7fc5efc8ca_terseLabel_en-US" xlink:label="lab_us-gaap_InterestBearingDomesticDepositCertificatesOfDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Certificates of deposit</link:label>
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    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_e1dcad74-4399-4a38-9f37-c06fdfefde19_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Depreciation_094b5de1-0093-4cf9-af09-6504af0616e8_verboseLabel_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Depreciation expense</link:label>
    <link:label id="lab_us-gaap_Depreciation_label_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Depreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Depreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Depreciation" xlink:to="lab_us-gaap_Depreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransferOfLoansHeldForSaleToPortfolioLoans1_d42009bb-dce8-462b-b3d0-152189d51bf8_terseLabel_en-US" xlink:label="lab_us-gaap_TransferOfLoansHeldForSaleToPortfolioLoans1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfer of loans from held for sale to held for investment</link:label>
    <link:label id="lab_us-gaap_TransferOfLoansHeldForSaleToPortfolioLoans1_label_en-US" xlink:label="lab_us-gaap_TransferOfLoansHeldForSaleToPortfolioLoans1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Transfer from Held-for-Sale to Held-in-Portfolio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferOfLoansHeldForSaleToPortfolioLoans1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransferOfLoansHeldForSaleToPortfolioLoans1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransferOfLoansHeldForSaleToPortfolioLoans1" xlink:to="lab_us-gaap_TransferOfLoansHeldForSaleToPortfolioLoans1" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_PennFedCapitalTrustIIIMember_409bd8e3-807d-4d6e-8f24-e0aa97791d94_terseLabel_en-US" xlink:label="lab_fbc_PennFedCapitalTrustIIIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PennFed Capital Trust III</link:label>
    <link:label id="lab_fbc_PennFedCapitalTrustIIIMember_label_en-US" xlink:label="lab_fbc_PennFedCapitalTrustIIIMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PennFed Capital Trust III [Member]</link:label>
    <link:label id="lab_fbc_PennFedCapitalTrustIIIMember_documentation_en-US" xlink:label="lab_fbc_PennFedCapitalTrustIIIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">PennFed Capital Trust III</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_PennFedCapitalTrustIIIMember" xlink:href="fbc-20251231.xsd#fbc_PennFedCapitalTrustIIIMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_PennFedCapitalTrustIIIMember" xlink:to="lab_fbc_PennFedCapitalTrustIIIMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract_63fc850e-ea03-4536-9bbd-7440fe8af49f_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of assets acquired:</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Asset [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectFinancingLeaseInterestIncome_17301d5d-cf4c-4828-830c-19fc88a152f6_terseLabel_en-US" xlink:label="lab_us-gaap_DirectFinancingLeaseInterestIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income on lease financing</link:label>
    <link:label id="lab_us-gaap_DirectFinancingLeaseInterestIncome_label_en-US" xlink:label="lab_us-gaap_DirectFinancingLeaseInterestIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Financing Lease, Interest Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectFinancingLeaseInterestIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DirectFinancingLeaseInterestIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectFinancingLeaseInterestIncome" xlink:to="lab_us-gaap_DirectFinancingLeaseInterestIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_ae9ac9c1-6d61-4412-966a-0b1971d6f310_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_d05f2f52-daee-4037-ac5d-1aa7210a01b9_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated year four</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Four, Originated, Three Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_4899a670-97f5-4f27-a52e-e3802bb8a291_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_MultiFamilyAndCommercialRealEstateMember_018f3c0b-e348-4ab9-b213-3a28669ff589_terseLabel_en-US" xlink:label="lab_fbc_MultiFamilyAndCommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-family and commercial real estate</link:label>
    <link:label id="lab_fbc_MultiFamilyAndCommercialRealEstateMember_label_en-US" xlink:label="lab_fbc_MultiFamilyAndCommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Multi-Family And Commercial Real Estate [Member]</link:label>
    <link:label id="lab_fbc_MultiFamilyAndCommercialRealEstateMember_documentation_en-US" xlink:label="lab_fbc_MultiFamilyAndCommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Multi-Family And Commercial Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_MultiFamilyAndCommercialRealEstateMember" xlink:href="fbc-20251231.xsd#fbc_MultiFamilyAndCommercialRealEstateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_MultiFamilyAndCommercialRealEstateMember" xlink:to="lab_fbc_MultiFamilyAndCommercialRealEstateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_DefinedBenefitPlanEquitySmallCapValueMember_2d49ee90-ad3d-4fe9-97c9-8436203bfa36_terseLabel_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquitySmallCapValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_fbc_DefinedBenefitPlanEquitySmallCapValueMember_label_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquitySmallCapValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Equity, Small Cap Value [Member]</link:label>
    <link:label id="lab_fbc_DefinedBenefitPlanEquitySmallCapValueMember_documentation_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquitySmallCapValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Equity, Small Cap Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_DefinedBenefitPlanEquitySmallCapValueMember" xlink:href="fbc-20251231.xsd#fbc_DefinedBenefitPlanEquitySmallCapValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_DefinedBenefitPlanEquitySmallCapValueMember" xlink:to="lab_fbc_DefinedBenefitPlanEquitySmallCapValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_db2bb256-9a26-4b70-93b6-883cbe5ce47a_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segment</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract_1cb8ec44-e21e-4032-96d9-474f65827e40_terseLabel_en-US" xlink:label="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets:</link:label>
    <link:label id="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Components of Deferred Tax Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComponentsOfDeferredTaxAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:to="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableIncomeAndExpenseOfBankOwnedLifeInsurance_389422c6-2a17-477a-894f-dc898de81461_terseLabel_en-US" xlink:label="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableIncomeAndExpenseOfBankOwnedLifeInsurance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-taxable expense of bank-owned life insurance</link:label>
    <link:label id="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableIncomeAndExpenseOfBankOwnedLifeInsurance_label_en-US" xlink:label="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableIncomeAndExpenseOfBankOwnedLifeInsurance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Non-Taxable Income And Expense Of Bank Owned Life Insurance</link:label>
    <link:label id="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableIncomeAndExpenseOfBankOwnedLifeInsurance_documentation_en-US" xlink:label="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableIncomeAndExpenseOfBankOwnedLifeInsurance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Non-Taxable Income And Expense Of Bank Owned Life Insurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableIncomeAndExpenseOfBankOwnedLifeInsurance" xlink:href="fbc-20251231.xsd#fbc_EffectiveIncomeTaxRateReconciliationNonTaxableIncomeAndExpenseOfBankOwnedLifeInsurance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableIncomeAndExpenseOfBankOwnedLifeInsurance" xlink:to="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableIncomeAndExpenseOfBankOwnedLifeInsurance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommercialRealEstateMember_3eedef57-5365-4323-b9e5-d1b044c5c2fe_terseLabel_en-US" xlink:label="lab_us-gaap_CommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial real estate</link:label>
    <link:label id="lab_us-gaap_CommercialRealEstateMember_label_en-US" xlink:label="lab_us-gaap_CommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Real Estate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialRealEstateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommercialRealEstateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommercialRealEstateMember" xlink:to="lab_us-gaap_CommercialRealEstateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_LeaseFinancingLoansMember_fee14b66-bddb-4287-b8ed-9ef1b981fcb8_terseLabel_en-US" xlink:label="lab_fbc_LeaseFinancingLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease financing</link:label>
    <link:label id="lab_fbc_LeaseFinancingLoansMember_label_en-US" xlink:label="lab_fbc_LeaseFinancingLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Financing Loans [Member]</link:label>
    <link:label id="lab_fbc_LeaseFinancingLoansMember_documentation_en-US" xlink:label="lab_fbc_LeaseFinancingLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease Financing Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_LeaseFinancingLoansMember" xlink:href="fbc-20251231.xsd#fbc_LeaseFinancingLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_LeaseFinancingLoansMember" xlink:to="lab_fbc_LeaseFinancingLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityDisclosureTextBlock_0016fdbc-53e5-46b6-9468-ff2051a321e2_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entities</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:to="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_FederalHomeLoanBankAdvanceMaturityAverageInterestRateYearSeven_968f072b-3564-4040-859e-9da02a3d4e43_terseLabel_en-US" xlink:label="lab_fbc_FederalHomeLoanBankAdvanceMaturityAverageInterestRateYearSeven" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2032</link:label>
    <link:label id="lab_fbc_FederalHomeLoanBankAdvanceMaturityAverageInterestRateYearSeven_label_en-US" xlink:label="lab_fbc_FederalHomeLoanBankAdvanceMaturityAverageInterestRateYearSeven" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advance, Maturity, Average Interest Rate, Year Seven</link:label>
    <link:label id="lab_fbc_FederalHomeLoanBankAdvanceMaturityAverageInterestRateYearSeven_documentation_en-US" xlink:label="lab_fbc_FederalHomeLoanBankAdvanceMaturityAverageInterestRateYearSeven" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advance, Maturity, Average Interest Rate, Year Seven</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FederalHomeLoanBankAdvanceMaturityAverageInterestRateYearSeven" xlink:href="fbc-20251231.xsd#fbc_FederalHomeLoanBankAdvanceMaturityAverageInterestRateYearSeven"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_FederalHomeLoanBankAdvanceMaturityAverageInterestRateYearSeven" xlink:to="lab_fbc_FederalHomeLoanBankAdvanceMaturityAverageInterestRateYearSeven" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_0cb4cf9a-ec0e-427c-b103-667a7e768287_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion_777f127f-1577-4e31-8406-1b1051ad53c0_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock issued upon conversion (in shares)</link:label>
    <link:label id="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion_label_en-US" xlink:label="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares, Common Stock Issuable Upon Conversion</link:label>
    <link:label id="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion_documentation_en-US" xlink:label="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares, Common Stock Issuable Upon Conversion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion" xlink:href="fbc-20251231.xsd#fbc_TemporaryEquitySharesCommonStockIssuableUponConversion"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion" xlink:to="lab_fbc_TemporaryEquitySharesCommonStockIssuableUponConversion" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter_0226a700-7bd9-4bb8-acf2-6c986bd8b5e0_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedThereafter"/>
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    <link:label id="lab_us-gaap_SubstandardMember_da69a686-87f0-44ce-a55c-40c19dffb69a_terseLabel_en-US" xlink:label="lab_us-gaap_SubstandardMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Substandard</link:label>
    <link:label id="lab_us-gaap_SubstandardMember_label_en-US" xlink:label="lab_us-gaap_SubstandardMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Substandard [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubstandardMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubstandardMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubstandardMember" xlink:to="lab_us-gaap_SubstandardMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_2e592113-f974-4e76-996a-0e8cd0b93005_totalLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total interest income</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndDividendIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:to="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SpecialMentionMember_e7026b3b-4458-49ff-bf78-4e0992e1e235_terseLabel_en-US" xlink:label="lab_us-gaap_SpecialMentionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Special Mention</link:label>
    <link:label id="lab_us-gaap_SpecialMentionMember_label_en-US" xlink:label="lab_us-gaap_SpecialMentionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Special Mention [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SpecialMentionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SpecialMentionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SpecialMentionMember" xlink:to="lab_us-gaap_SpecialMentionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_2561ddc4-d6ed-4653-96bd-449f2d840c97_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesPeriodPastDueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStock_83a45c60-7207-4a39-b0e6-2c455f3badec_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on common stock</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStock" xlink:to="lab_us-gaap_DividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFour_0991313c-e5ef-4fb7-bebb-d6bfceec846f_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFour_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Expected Future Benefit Payment, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFour" xlink:to="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentsOwnedAtFairValue_ef29d550-bd1f-495d-9282-2253ddfef073_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total collateral-dependent loans held for investment</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentsOwnedAtFairValue_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments, Owned, at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentsOwnedAtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentsOwnedAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentsOwnedAtFairValue" xlink:to="lab_us-gaap_FinancialInstrumentsOwnedAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_bc735ec7-7289-4959-8551-0ca22173fa1c_terseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans and leases held for investment, net</link:label>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Receivable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansReceivableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:to="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_MortgageServicingRightsMember_bd9d9098-3d00-4ff2-8687-7f555bf842bd_terseLabel_en-US" xlink:label="lab_fbc_MortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights</link:label>
    <link:label id="lab_fbc_MortgageServicingRightsMember_4441b81f-a12b-43b7-9e6a-205633b45bbd_verboseLabel_en-US" xlink:label="lab_fbc_MortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights</link:label>
    <link:label id="lab_fbc_MortgageServicingRightsMember_label_en-US" xlink:label="lab_fbc_MortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights [Member]</link:label>
    <link:label id="lab_fbc_MortgageServicingRightsMember_documentation_en-US" xlink:label="lab_fbc_MortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative assets or liabilities which hedge the risk of overall changes in fair value of MSRs through the use of various derivatives including purchases of forward contracts on securities of Fannie Mae and Freddie Mac, the purchase/sale of U.S. Treasury futures contracts and the purchase/sale of euro dollar future contracts. These are accounted for as non-designated hedges.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_MortgageServicingRightsMember" xlink:href="fbc-20251231.xsd#fbc_MortgageServicingRightsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_MortgageServicingRightsMember" xlink:to="lab_fbc_MortgageServicingRightsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_IndividualAxis"/>
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    <link:label id="lab_us-gaap_DefinedContributionPlanCostRecognized_7e8b186a-2417-4f3d-92f8-19201c4b7fa3_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">401(k) plan contributions by employer</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanCostRecognized_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanCostRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanCostRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedContributionPlanCostRecognized" xlink:to="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_4528301c-9104-4aff-96c9-7daaa4baffad_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:to="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_7dcd1f19-9886-4c10-b860-df18881092e2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cash dividends paid on common stock</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Ordinary Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:to="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInLoansHeldForSale_854c285d-6f94-4dc2-a92a-092d4586f0a6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInLoansHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in loans held for sale, net</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInLoansHeldForSale_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Loan, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInLoansHeldForSale" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInLoansHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInLoansHeldForSale" xlink:to="lab_us-gaap_IncreaseDecreaseInLoansHeldForSale" xlink:type="arc" order="1"/>
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    <link:label id="lab_fbc_NoncumulativePreferredStockSeriesAMember_2d38e487-1a0e-4c7b-8872-f39e7571a5be_terseLabel_en-US" xlink:label="lab_fbc_NoncumulativePreferredStockSeriesAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">6.375% Fixed-to-Floating Rate Perpetual Noncumulative Series A</link:label>
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    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacy_1734095c-0bba-43f5-bd05-767d781f5009_terseLabel_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum for capital adequacy, amount</link:label>
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    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_983baa4e-25a1-4b36-b991-2c26d7dd6cb7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments of long-term debt issuances/advances</link:label>
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    <link:label id="lab_fbc_FinancingReceivableRelatedAllowance_770db3f5-4601-403d-bbc7-cc5e2985b6fe_terseLabel_en-US" xlink:label="lab_fbc_FinancingReceivableRelatedAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Allowance</link:label>
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    <link:label id="lab_fbc_FinancingReceivableRelatedAllowance_documentation_en-US" xlink:label="lab_fbc_FinancingReceivableRelatedAllowance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Related Allowance</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract_db860b3d-fb87-4a1b-bf26-67c961a4779b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffByOriginationYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year to date gross charge-offs</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestExpense" xlink:to="lab_us-gaap_NoninterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketableSecurities_9990c375-530b-455d-b248-cce9d12bf22b_terseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total securities</link:label>
    <link:label id="lab_us-gaap_MarketableSecurities_label_en-US" xlink:label="lab_us-gaap_MarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MarketableSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketableSecurities" xlink:to="lab_us-gaap_MarketableSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion_bd54044a-b1b2-48b3-84bb-17cad0fe8060_terseLabel_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible stock (in shares)</link:label>
    <link:label id="lab_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion_label_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Preferred Stock, Shares Issued upon Conversion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion" xlink:to="lab_us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_41e42c8c-6de3-45dc-b54b-ff8740182384_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss carryforwards</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwards"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesTextBlock_05e88030-c1f0-40a1-993e-7051a526f938_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Credit Losses on Loans and Leases</link:label>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesTextBlock_label_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance for Credit Losses [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForCreditLossesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForCreditLossesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForCreditLossesTextBlock" xlink:to="lab_us-gaap_AllowanceForCreditLossesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_f58f5a28-e20e-4423-9b14-fa22382aaf08_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashMergerRelatedCosts_66552724-bf20-4b6a-8eb7-ea6303fb3ae7_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashMergerRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Merger-related and restructuring expenses</link:label>
    <link:label id="lab_us-gaap_NoncashMergerRelatedCosts_label_en-US" xlink:label="lab_us-gaap_NoncashMergerRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Merger Related Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashMergerRelatedCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncashMergerRelatedCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashMergerRelatedCosts" xlink:to="lab_us-gaap_NoncashMergerRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestIncomeAbstract_f81a88ae-bab8-4ce7-8b82-23afc496e65c_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NON-INTEREST INCOME:</link:label>
    <link:label id="lab_us-gaap_NoninterestIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_NoninterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncomeAbstract" xlink:to="lab_us-gaap_NoninterestIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_CombinationInterestRateReductionAndTermPaymentExtensionDelayMember_019c24da-ab36-7368-998d-5627a9df14e3_terseLabel_en-US" xlink:label="lab_fbc_CombinationInterestRateReductionAndTermPaymentExtensionDelayMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Combination - Interest Rate Reduction and Term/Payment Extension/Delay</link:label>
    <link:label id="lab_fbc_CombinationInterestRateReductionAndTermPaymentExtensionDelayMember_label_en-US" xlink:label="lab_fbc_CombinationInterestRateReductionAndTermPaymentExtensionDelayMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Combination - Interest Rate Reduction and Term/Payment Extension/Delay [Member]</link:label>
    <link:label id="lab_fbc_CombinationInterestRateReductionAndTermPaymentExtensionDelayMember_documentation_en-US" xlink:label="lab_fbc_CombinationInterestRateReductionAndTermPaymentExtensionDelayMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Combination - Interest Rate Reduction and Term/Payment Extension/Delay</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_CombinationInterestRateReductionAndTermPaymentExtensionDelayMember" xlink:href="fbc-20251231.xsd#fbc_CombinationInterestRateReductionAndTermPaymentExtensionDelayMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_CombinationInterestRateReductionAndTermPaymentExtensionDelayMember" xlink:to="lab_fbc_CombinationInterestRateReductionAndTermPaymentExtensionDelayMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateRollingYearParValueAbstract_93ac17eb-b1f8-46ba-b4c5-838c41df7b23_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateRollingYearParValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateRollingYearParValueAbstract_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateRollingYearParValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advances, Par Value, Earlier of Contractual Maturity or Next Put or Convert Date, Rolling Year [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateRollingYearParValueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateRollingYearParValueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateRollingYearParValueAbstract" xlink:to="lab_us-gaap_FederalHomeLoanBankAdvancesEarlierOfContractualMaturityOrNextPutOrConvertDateRollingYearParValueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLiabilities_d10114d0-2958-4df2-9cf7-f8e8ee2ce5bd_totalLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities assumed</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLiabilities_label_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Liabilities</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLiabilities_documentation_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLiabilities" xlink:href="fbc-20251231.xsd#fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLiabilities" xlink:to="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_FlagstarStatutoryTrustIIMember_07146b1e-bd4c-49b2-9ac6-d38a21f85b46_terseLabel_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustIIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust II</link:label>
    <link:label id="lab_fbc_FlagstarStatutoryTrustIIMember_label_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustIIMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust II [Member]</link:label>
    <link:label id="lab_fbc_FlagstarStatutoryTrustIIMember_documentation_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustIIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust II</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FlagstarStatutoryTrustIIMember" xlink:href="fbc-20251231.xsd#fbc_FlagstarStatutoryTrustIIMember"/>
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    <link:label id="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare_3bfbaece-9fdf-4dfc-9833-b1498027efc9_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liquidation preference per share (in usd per share)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Liquidation Preference Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityLiquidationPreferencePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:to="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesDPreferredStockMember_019c245a-8741-722b-a4cb-22bbd45bc42e_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesDPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series D Preferred Stock</link:label>
    <link:label id="lab_us-gaap_SeriesDPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesDPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series D Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesDPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeriesDPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesDPreferredStockMember" xlink:to="lab_us-gaap_SeriesDPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo_11b7d979-6309-4ce4-a8f1-a1fcd89f039e_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Expected Future Benefit Payment, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo" xlink:to="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_SoftwareExpense_019be989-2338-7bd0-8405-d436d040bfd4_terseLabel_en-US" xlink:label="lab_fbc_SoftwareExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Software expense</link:label>
    <link:label id="lab_fbc_SoftwareExpense_label_en-US" xlink:label="lab_fbc_SoftwareExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Software Expense</link:label>
    <link:label id="lab_fbc_SoftwareExpense_documentation_en-US" xlink:label="lab_fbc_SoftwareExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Software Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_SoftwareExpense" xlink:href="fbc-20251231.xsd#fbc_SoftwareExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_SoftwareExpense" xlink:to="lab_fbc_SoftwareExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_43d7a837-9f61-41b0-b0b5-53809aa10988_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_WarrantOrRightCouponRate_5f015c5b-dc24-4d5e-a5bb-86cda701a23e_terseLabel_en-US" xlink:label="lab_fbc_WarrantOrRightCouponRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant or right, coupon rate</link:label>
    <link:label id="lab_fbc_WarrantOrRightCouponRate_label_en-US" xlink:label="lab_fbc_WarrantOrRightCouponRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrant Or Right, Coupon Rate</link:label>
    <link:label id="lab_fbc_WarrantOrRightCouponRate_documentation_en-US" xlink:label="lab_fbc_WarrantOrRightCouponRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrant Or Right, Coupon Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_WarrantOrRightCouponRate" xlink:href="fbc-20251231.xsd#fbc_WarrantOrRightCouponRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_WarrantOrRightCouponRate" xlink:to="lab_fbc_WarrantOrRightCouponRate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoName"/>
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    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
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    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_c16e4911-8e08-4d52-82df-184ca059001c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
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    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_95bb1e8f-9917-4985-a09f-b25453557a4e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Loans Held for Investment</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Credit Quality Indicators [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock"/>
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    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingAggtErrCompAmt"/>
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    <link:label id="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable_63e8dd17-bb2f-456b-9766-7b778f55cee1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:to="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy_af2b3471-c9dd-445f-911d-d187b57b759a_terseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum for capital adequacy, amount</link:label>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy_label_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Leverage Capital, Capital Adequacy, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneLeverageCapitalRequiredForCapitalAdequacy"/>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesParValue_2e648703-3a29-4aab-aa6a-c84805c35c1b_totalLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesParValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total FHLB advances</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesParValue_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesParValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advances, Par Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesParValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FederalHomeLoanBankAdvancesParValue"/>
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    <link:label id="lab_us-gaap_NoninterestBearingDepositLiabilities_658b21c8-37c3-48e3-9281-b5b4005a5b11_verboseLabel_en-US" xlink:label="lab_us-gaap_NoninterestBearingDepositLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Non-interest-bearing accounts</link:label>
    <link:label id="lab_us-gaap_NoninterestBearingDepositLiabilities_a9e23969-d88a-49bc-a6f8-e3d4ac2e8b52_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestBearingDepositLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-interest-bearing accounts</link:label>
    <link:label id="lab_us-gaap_NoninterestBearingDepositLiabilities_label_en-US" xlink:label="lab_us-gaap_NoninterestBearingDepositLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest-Bearing Deposit Liabilities</link:label>
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    <link:label id="lab_fbc_FlagstarStatutoryTrustVIIMember_6d623b87-8e80-45e4-90fa-5f832b432b7b_terseLabel_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustVIIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust VII</link:label>
    <link:label id="lab_fbc_FlagstarStatutoryTrustVIIMember_label_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustVIIMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust VII [Member]</link:label>
    <link:label id="lab_fbc_FlagstarStatutoryTrustVIIMember_documentation_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustVIIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust VII</link:label>
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    <link:label id="lab_us-gaap_MortgageBackedSecuritiesOtherMember_9c888558-235c-4a05-916e-34282f049db1_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage-backed securities forwards</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesOtherMember_3fcd1ffb-665c-417b-8ef8-077c62bfefe9_verboseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesOtherMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgage-backed securities forwards</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesOtherMember_label_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage-Backed Securities, Other [Member]</link:label>
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    <link:label id="lab_fbc_NewYorkCommunityCapitalTrustXIMember_3ebd9970-01d8-45a4-aef7-ea74e018a55a_terseLabel_en-US" xlink:label="lab_fbc_NewYorkCommunityCapitalTrustXIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New York Community Capital Trust XI</link:label>
    <link:label id="lab_fbc_NewYorkCommunityCapitalTrustXIMember_label_en-US" xlink:label="lab_fbc_NewYorkCommunityCapitalTrustXIMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New York Community Capital Trust XI [Member]</link:label>
    <link:label id="lab_fbc_NewYorkCommunityCapitalTrustXIMember_documentation_en-US" xlink:label="lab_fbc_NewYorkCommunityCapitalTrustXIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New York Community Capital Trust XI</link:label>
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    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_73a17d62-1171-4519-b8ba-204d8374873a_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offering price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Exercise Price of Warrants or Rights</link:label>
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    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_aca6db59-8abf-42d5-a9f0-f4b4fb7bf4bb_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock - Series B</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_8236cea5-7e7a-469e-8a41-77544f0bb73b_periodStartLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_24bbb971-b924-44e7-b3a1-8e1ae625ebca_periodEndLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Carrying Amount, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent"/>
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    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardExrcPrice"/>
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    <link:label id="lab_dei_EntityFilerCategory_eed47b9e-4940-4d58-9f67-11ec20bb9dfe_verboseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFilerCategory"/>
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    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacyToRiskWeightedAssets_47bddd00-4367-4d54-9af4-33b904371c72_terseLabel_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum for capital adequacy, ratio</link:label>
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    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
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    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_054b5716-b418-4e1e-9d1a-de81ac7fb7fa_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
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    <link:label id="lab_us-gaap_StockIssued1_851e3dd3-94a9-4122-90b1-c0a60d8ccb41_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssued1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares issued for restricted stock awards</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]</link:label>
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    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_9b78153a-396f-46b6-954c-c571f2d44321_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InternalCreditAssessmentDomain"/>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_db2981da-afd6-492a-8db4-47db8730daf0_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Derivative and Hedging Activities</link:label>
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    <link:label id="lab_us-gaap_OtherLiabilitiesMember_8018eb56-511a-49b5-b90d-87fe35bfedcc_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesMember_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesMember" xlink:to="lab_us-gaap_OtherLiabilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilityNotRecognizedAmountOfUnrecognizedDeferredTaxLiabilityBadDebtReserveForTaxPurposesOfQualifiedLender_51353e1d-0df3-4d11-baa6-687ed82c009b_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilityNotRecognizedAmountOfUnrecognizedDeferredTaxLiabilityBadDebtReserveForTaxPurposesOfQualifiedLender" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal deferred tax liability, bad debt reserve</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_3e954657-84ea-4039-a324-4ff6d2d5ef92_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less than Twelve Months</link:label>
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    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalToRiskWeightedAssets_df7c5c87-683b-474e-8218-58f9de487248_terseLabel_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total capital, ratio</link:label>
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    <link:label id="lab_us-gaap_LongTermDebtFairValue_4a9ea9a1-c4c1-4e56-94b3-1a426706eea9_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowed funds</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements_0a5b1b18-f072-4f34-876c-80736b4ef048_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Leasing Arrangements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesLeasingArrangements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_2d83dc9f-2fe0-488d-af0f-06b5f6d37c64_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend rate percentage</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockDividendRatePercentage"/>
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    <link:label id="lab_us-gaap_FeeIncome_e77af51b-f321-4e7b-af90-822969a7f581_terseLabel_en-US" xlink:label="lab_us-gaap_FeeIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fee income</link:label>
    <link:label id="lab_us-gaap_FeeIncome_label_en-US" xlink:label="lab_us-gaap_FeeIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fee Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FeeIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FeeIncome"/>
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    <link:label id="lab_fbc_FurnitureFixturesAndEquipmentMember_019be9c3-dae0-72b2-8e3d-c537ad4f7524_terseLabel_en-US" xlink:label="lab_fbc_FurnitureFixturesAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Furniture, fixtures and equipment</link:label>
    <link:label id="lab_fbc_FurnitureFixturesAndEquipmentMember_label_en-US" xlink:label="lab_fbc_FurnitureFixturesAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Furniture, Fixtures And Equipment [Member]</link:label>
    <link:label id="lab_fbc_FurnitureFixturesAndEquipmentMember_documentation_en-US" xlink:label="lab_fbc_FurnitureFixturesAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Furniture, Fixtures And Equipment</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_FurnitureFixturesAndEquipmentMember" xlink:to="lab_fbc_FurnitureFixturesAndEquipmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_42681ce8-7e3f-4c06-97ad-55c4162e6a59_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIntangibleAssetsMember_c96650df-39c9-42b9-8fc2-3a6bc9869260_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other intangible assets</link:label>
    <link:label id="lab_us-gaap_OtherIntangibleAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Intangible Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIntangibleAssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherIntangibleAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIntangibleAssetsMember" xlink:to="lab_us-gaap_OtherIntangibleAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_SubservicingAssetAtFairValueIncomeAmount_86a4184f-5878-41ca-b1c4-bd816df727c0_totalLabel_en-US" xlink:label="lab_fbc_SubservicingAssetAtFairValueIncomeAmount" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total income (loss) on mortgage loans subserviced, included in loan administration income</link:label>
    <link:label id="lab_fbc_SubservicingAssetAtFairValueIncomeAmount_label_en-US" xlink:label="lab_fbc_SubservicingAssetAtFairValueIncomeAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subservicing Asset At Fair Value, Income, Amount</link:label>
    <link:label id="lab_fbc_SubservicingAssetAtFairValueIncomeAmount_documentation_en-US" xlink:label="lab_fbc_SubservicingAssetAtFairValueIncomeAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The amount of income earned from subservicing an asset at fair value.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_SubservicingAssetAtFairValueIncomeAmount" xlink:href="fbc-20251231.xsd#fbc_SubservicingAssetAtFairValueIncomeAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_SubservicingAssetAtFairValueIncomeAmount" xlink:to="lab_fbc_SubservicingAssetAtFairValueIncomeAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnOilAndGasHedgingActivity_69d813c7-cf18-4ffc-b2d7-0bd171f2171f_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnOilAndGasHedgingActivity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on MSR derivatives</link:label>
    <link:label id="lab_us-gaap_GainLossOnOilAndGasHedgingActivity_label_en-US" xlink:label="lab_us-gaap_GainLossOnOilAndGasHedgingActivity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Hedging Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnOilAndGasHedgingActivity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnOilAndGasHedgingActivity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnOilAndGasHedgingActivity" xlink:to="lab_us-gaap_GainLossOnOilAndGasHedgingActivity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_4b2bdf7a-b2d9-4afb-bea4-c972a2df9449_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Unrealized Gain</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
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    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_70ad6082-e4e2-4d61-b4fc-e4975b29fc47_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Offsetting Assets</link:label>
    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffsettingAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:to="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValuePeriodIncreaseDecrease_eaabb2ef-4f72-433e-b97a-f76325c7fc4e_verboseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValuePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Changes in estimates of fair value due to interest rate risk</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValuePeriodIncreaseDecrease_a9cff54b-86ff-46d7-b998-0b67c7ac0ecd_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValuePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in fair value due to interest rate risk</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValuePeriodIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValuePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Fair Value, Period Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtFairValuePeriodIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAtFairValuePeriodIncreaseDecrease"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_c5d0e7e8-6b85-4e58-ba35-73ae92e30e77_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax_89ae9090-5cb4-4217-8682-66a4d3c9d2e9_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amount of gain recognized in accumulated other comprehensive loss</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), before Reclassification and Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAndTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_3008d524-5eb5-4518-bdac-ad734df834ef_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_271f8efd-84b6-4729-8978-ae54b2a37708_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasehold improvements</link:label>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_label_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leasehold Improvements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseholdImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseholdImprovementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseholdImprovementsMember" xlink:to="lab_us-gaap_LeaseholdImprovementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFederalHomeLoanBankAdvancesByBranchOfFHLBBankTextBlock_32fb7207-0c7c-48d0-8cf4-60d2454cb07e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFederalHomeLoanBankAdvancesByBranchOfFHLBBankTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Federal Home Loan Bank, Advance, Branch of FHLBank</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFederalHomeLoanBankAdvancesByBranchOfFHLBBankTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFederalHomeLoanBankAdvancesByBranchOfFHLBBankTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advance, Branch of FHLBank [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFederalHomeLoanBankAdvancesByBranchOfFHLBBankTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFederalHomeLoanBankAdvancesByBranchOfFHLBBankTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFederalHomeLoanBankAdvancesByBranchOfFHLBBankTextBlock" xlink:to="lab_us-gaap_ScheduleOfFederalHomeLoanBankAdvancesByBranchOfFHLBBankTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems_942c718a-a1b7-40d8-b6bd-bd3791e2c228_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan Disclosure [Line Items]</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:to="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesGeneralDebtObligationsDisclosuresRepaymentAndPenalties_37652d33-5503-46c0-af7b-2f03af27b39b_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesGeneralDebtObligationsDisclosuresRepaymentAndPenalties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayment of FHLB loan advances</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_fbb29789-de0b-484a-9674-25c482e5e077_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
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    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
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    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_84dc0781-aead-4d29-b283-0c9259ba7749_verboseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Estimated Fair Value</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
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    <link:label id="lab_us-gaap_RetirementPlanTypeDomain_b91c0374-2879-4142-88ea-1f133d8e4cdf_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Domain]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanTypeDomain_label_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Domain]</link:label>
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    <link:label id="lab_us-gaap_PerformingFinancingReceivableMember_f1fe4be3-73f0-45fc-bef7-d3130557ec40_verboseLabel_en-US" xlink:label="lab_us-gaap_PerformingFinancingReceivableMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accrual loans:</link:label>
    <link:label id="lab_us-gaap_PerformingFinancingReceivableMember_label_en-US" xlink:label="lab_us-gaap_PerformingFinancingReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performing Financial Instruments [Member]</link:label>
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    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems_704b759b-8bd6-43d9-8f21-119c1bc0bc26_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Quantitative Disclosures</link:label>
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    <link:label id="lab_fbc_NonAccrualMember_c368c087-f680-480f-96d9-c3d9dca75951_terseLabel_en-US" xlink:label="lab_fbc_NonAccrualMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-accrual</link:label>
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    <link:label id="lab_fbc_NonAccrualMember_documentation_en-US" xlink:label="lab_fbc_NonAccrualMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Accrual</link:label>
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    <link:label id="lab_fbc_FlagstarStatutoryTrustIVMember_8ca21304-4204-444d-bb73-4d2218e421aa_terseLabel_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustIVMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust IV</link:label>
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    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLoansHeldForInvestment_97c4b773-0353-4121-be0f-e47fcb5d2198_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held for investment:</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedAmortizationNextFiscalYear_ac714705-d908-4cd7-8bcb-8d010e1018ab_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedAmortizationNextFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized net actuarial loss</link:label>
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    <link:label id="lab_us-gaap_ExcessCapitalToRiskWeightedAssets_fd566b20-39b4-4e0f-9578-ce797d1f5df2_terseLabel_en-US" xlink:label="lab_us-gaap_ExcessCapitalToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excess, ratio</link:label>
    <link:label id="lab_us-gaap_ExcessCapitalToRiskWeightedAssets_label_en-US" xlink:label="lab_us-gaap_ExcessCapitalToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital Ratio, Excess, Actual</link:label>
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    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCoreDepositAndOtherIntangibleAssets_22d7164f-c112-4958-ab5e-dbfd9d36467c_terseLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentCoreDepositAndOtherIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CDI and other intangible assets</link:label>
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    <link:label id="lab_dei_DocumentsIncorporatedByReferenceTextBlock_58634519-8c79-4bd9-acc0-532704af5f5e_terseLabel_en-US" xlink:label="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Documents Incorporated by Reference</link:label>
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    <link:label id="lab_dei_EntitySmallBusiness_ac418b35-a542-44e2-b257-49acc64a151c_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
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    <link:label id="lab_us-gaap_AccountsPayableInterestBearingInterestRate_019c8ab2-3fa5-7588-a4b2-bd6587d95921_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableInterestBearingInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest annually on escrow accounts</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableInterestBearingInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableInterestBearingInterestRate"/>
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    <link:label id="lab_us-gaap_PreferredStockConvertibleConversionPrice_ed8bf677-3e12-41c1-8bbd-77e64ce8c85e_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockConvertibleConversionPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockConvertibleConversionPrice_label_en-US" xlink:label="lab_us-gaap_PreferredStockConvertibleConversionPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Convertible, Conversion Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockConvertibleConversionPrice" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockConvertibleConversionPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockConvertibleConversionPrice" xlink:to="lab_us-gaap_PreferredStockConvertibleConversionPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_199d7647-f461-4113-a464-1e9c657ff057_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Contingency [Line Items]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:to="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_b047a04e-fd17-43b4-a4d0-88acd06101cf_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense interest and penalties</link:label>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_label_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits, Income Tax Penalties and Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense"/>
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    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_47769643-825e-45f6-bfbe-ad426c97cb7a_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
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    <link:label id="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit_ab4242c0-f690-4467-90de-b333aacedff8_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State and local &#8211; current</link:label>
    <link:label id="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current State and Local Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentStateAndLocalTaxExpenseBenefit"/>
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    <link:label id="lab_dei_DocumentTransitionReport_8c8a8d60-7b5a-46bc-8178-dcd10db78e8a_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_f3ae86c7-34c3-4f9b-9284-0c2763fe96ba_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_019c4d3a-afcf-7e2c-ab86-9630ecd50685_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from one to five years</link:label>
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    <link:label id="lab_us-gaap_CorporateNoteSecuritiesMember_6953f9b9-5a3f-40ea-92f0-338df5b94b39_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateNoteSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital trust notes</link:label>
    <link:label id="lab_us-gaap_CorporateNoteSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_CorporateNoteSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Note Securities [Member]</link:label>
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    <link:label id="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare_bf614d01-0ba6-431b-9161-369f3d3210e7_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock, shares average price (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_FirstMortgageMember_fab94b05-83fc-4669-91de-1ee5089ce3b6_netLabel_en-US" xlink:label="lab_us-gaap_FirstMortgageMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Residential First Mortgage</link:label>
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    <link:label id="lab_dei_DocumentType_f7577f49-8f8b-4cf4-a42e-9cb80cc310b5_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_50632562-c919-4c96-8b57-082fb3441071_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Unobservable Inputs (Level 3)</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract_3bb20db3-06d7-43ce-9a0d-25ef7c0bd0da_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableforSaleUnrealizedLossPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
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    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapital_321670fa-b6f3-414e-8b74-9d092e1e5f0d_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Paid-in capital in excess of par</link:label>
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    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableUndiscountedExcessAmount_fc8772b8-e0f0-43e1-85cd-d21c2df1a581_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivableUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: unearned income</link:label>
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    <link:label id="lab_srt_BrokersAndDealersAbstract_label_en-US" xlink:label="lab_srt_BrokersAndDealersAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Broker-Dealer [Abstract]</link:label>
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    <link:label id="lab_fbc_MunicipalBondsForeignNotesAndCapitalTrustMember_019c8a48-b0ba-7f3c-9910-7a184ef757fd_terseLabel_en-US" xlink:label="lab_fbc_MunicipalBondsForeignNotesAndCapitalTrustMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Municipal bonds, foreign notes, and capital trust</link:label>
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    <link:label id="lab_fbc_DefinedBenefitPlanExpectedFutureBenefitPayment_1a848b5c-2cdc-458b-9eef-8740053fcf83_totalLabel_en-US" xlink:label="lab_fbc_DefinedBenefitPlanExpectedFutureBenefitPayment" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_353a4cdb-b167-4fd9-bac1-ec80f23dcde8_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net (loss) attributable / net income available to common stockholders</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivablePurchasedWithCreditDeteriorationAmountAtParValue_35e7a340-05f9-4a4d-a98e-d3164fcf1642_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablePurchasedWithCreditDeteriorationAmountAtParValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Par value (UPB)</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_9ec3c124-8646-4d63-8912-d3b2b0f85701_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other comprehensive gain (loss), net of tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_599abbfe-da9b-44d7-b75b-cab72daa6481_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive (loss) income, net of tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock_1663f671-51be-4620-ae0f-ec0a94ebd3e3_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Gain (Loss) Recognized in Income on Derivative Instruments</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPast12Months_9a32fe09-f64f-41c5-a5ae-2b302dce6f01_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPast12Months" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_fcaa9326-5081-4d77-ba96-0f31baf510be_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quoted Prices in Active Markets for Identical Assets (Level 1)</link:label>
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    <link:label id="lab_us-gaap_SharesOutstanding_5e33ba2c-1491-4635-8d6c-068bb5f18cef_periodStartLabel_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
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    <link:label id="lab_fbc_FDICMember_eff0e9cb-f2e8-4698-943f-f4e01d4aeb98_terseLabel_en-US" xlink:label="lab_fbc_FDICMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FDIC</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareDiluted_93595b9c-57d8-4c02-9cbf-c6210c3791e5_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (loss) earnings per common share (in usd per share)</link:label>
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    <link:label id="lab_us-gaap_FederalDepositInsuranceCorporationPremiumExpense_54789812-4dfc-451e-b747-5b097b8b865a_terseLabel_en-US" xlink:label="lab_us-gaap_FederalDepositInsuranceCorporationPremiumExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FDIC insurance</link:label>
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    <link:label id="lab_fbc_NewYorkCityMember_019c4be3-a0a4-7090-9bf9-14f9e031906a_terseLabel_en-US" xlink:label="lab_fbc_NewYorkCityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New York City</link:label>
    <link:label id="lab_fbc_NewYorkCityMember_label_en-US" xlink:label="lab_fbc_NewYorkCityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New York City [Member]</link:label>
    <link:label id="lab_fbc_NewYorkCityMember_documentation_en-US" xlink:label="lab_fbc_NewYorkCityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New York City</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NewYorkCityMember" xlink:href="fbc-20251231.xsd#fbc_NewYorkCityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_NewYorkCityMember" xlink:to="lab_fbc_NewYorkCityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis_45c19819-9e04-4aff-9326-5abd9d4b1f17_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Axis]</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:to="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_FinancingReceivablePaymentPerformancePeriodThreshold_6bebf66e-1134-461e-8748-a30e6e29bc29_terseLabel_en-US" xlink:label="lab_fbc_FinancingReceivablePaymentPerformancePeriodThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payment performance period threshold</link:label>
    <link:label id="lab_fbc_FinancingReceivablePaymentPerformancePeriodThreshold_label_en-US" xlink:label="lab_fbc_FinancingReceivablePaymentPerformancePeriodThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Payment Performance Period Threshold</link:label>
    <link:label id="lab_fbc_FinancingReceivablePaymentPerformancePeriodThreshold_documentation_en-US" xlink:label="lab_fbc_FinancingReceivablePaymentPerformancePeriodThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Payment Performance Period Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FinancingReceivablePaymentPerformancePeriodThreshold" xlink:href="fbc-20251231.xsd#fbc_FinancingReceivablePaymentPerformancePeriodThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_FinancingReceivablePaymentPerformancePeriodThreshold" xlink:to="lab_fbc_FinancingReceivablePaymentPerformancePeriodThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_75f9430e-0485-465b-be65-c116578706d3_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cash investing and financing activities:</link:label>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_019c4d3a-afcf-76c8-89b8-00cb57a9888c_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from five to ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod_c5ffa73d-63d3-4e2c-992f-110e166a111b_netLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Loans modified</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod_aa86cd2a-1c57-4191-aa9b-57dd0ec4788b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reduced Amortized Cost Basis</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Modified in Period, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansReceivableHeldForSaleAmount_ed0d8230-f71f-49b0-aef7-e1344dad422c_terseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableHeldForSaleAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held for sale</link:label>
    <link:label id="lab_us-gaap_LoansReceivableHeldForSaleAmount_44b4d0e3-2b14-45e1-8f02-ed4dfc7297f4_netLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableHeldForSaleAmount" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Loans held for sale</link:label>
    <link:label id="lab_us-gaap_LoansReceivableHeldForSaleAmount_label_en-US" xlink:label="lab_us-gaap_LoansReceivableHeldForSaleAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansReceivableHeldForSaleAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansReceivableHeldForSaleAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansReceivableHeldForSaleAmount" xlink:to="lab_us-gaap_LoansReceivableHeldForSaleAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_265f7a9a-d9b4-4dc6-bff0-6421b194dfa9_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonShares" xlink:to="lab_us-gaap_TreasuryStockCommonShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_2c35a640-453a-46d8-abb2-2fc4f4f01235_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing Asset, Fair Value, Change in Fair Value, Other, Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset, Fair Value, Change in Fair Value, Other, Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:to="lab_us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived_a4c50057-28d3-4035-94dc-48a545350d1c_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total state and local</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, State and Local, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:to="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_OtherLoanCommitmentsMember_489caf46-70eb-4ea6-848e-be535a25ca6f_terseLabel_en-US" xlink:label="lab_fbc_OtherLoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_fbc_OtherLoanCommitmentsMember_5ad44e9a-0c5c-42ef-88fb-f3dd2898be4b_verboseLabel_en-US" xlink:label="lab_fbc_OtherLoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other loan commitments</link:label>
    <link:label id="lab_fbc_OtherLoanCommitmentsMember_label_en-US" xlink:label="lab_fbc_OtherLoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Loan Commitments [Member]</link:label>
    <link:label id="lab_fbc_OtherLoanCommitmentsMember_documentation_en-US" xlink:label="lab_fbc_OtherLoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Loan Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_OtherLoanCommitmentsMember" xlink:href="fbc-20251231.xsd#fbc_OtherLoanCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_OtherLoanCommitmentsMember" xlink:to="lab_fbc_OtherLoanCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_99b32b1a-0b82-4491-83df-ecf969918195_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:to="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorLocation_961d7052-8034-4900-843c-bf48d755371c_terseLabel_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:label id="lab_dei_AuditorLocation_label_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorLocation" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorLocation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorLocation" xlink:to="lab_dei_AuditorLocation" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_OneToFourFamilyFirstMortgageLoanMember_0766dc84-6e26-4a6a-b3d8-24745b1001c3_terseLabel_en-US" xlink:label="lab_fbc_OneToFourFamilyFirstMortgageLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">One-to-four family first mortgage</link:label>
    <link:label id="lab_fbc_OneToFourFamilyFirstMortgageLoanMember_label_en-US" xlink:label="lab_fbc_OneToFourFamilyFirstMortgageLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">One-to-Four Family First Mortgage Loan [Member]</link:label>
    <link:label id="lab_fbc_OneToFourFamilyFirstMortgageLoanMember_documentation_en-US" xlink:label="lab_fbc_OneToFourFamilyFirstMortgageLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">One-to-Four Family First Mortgage Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_OneToFourFamilyFirstMortgageLoanMember" xlink:href="fbc-20251231.xsd#fbc_OneToFourFamilyFirstMortgageLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_OneToFourFamilyFirstMortgageLoanMember" xlink:to="lab_fbc_OneToFourFamilyFirstMortgageLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CoreDepositsMember_04c90fd0-df2b-495a-952a-18a6ab6e11bc_terseLabel_en-US" xlink:label="lab_us-gaap_CoreDepositsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Core deposit intangible</link:label>
    <link:label id="lab_us-gaap_CoreDepositsMember_label_en-US" xlink:label="lab_us-gaap_CoreDepositsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Core Deposits [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CoreDepositsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CoreDepositsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CoreDepositsMember" xlink:to="lab_us-gaap_CoreDepositsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_f53d91b1-2e07-46e7-b2e0-c7528d789762_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Not Primary Beneficiary</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Not Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAdditions_80de5959-797a-49a2-a909-01577ab15d37_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAdditions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additions from loans sold with servicing retained</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAdditions_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAdditions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Fair Value, Additions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtFairValueAdditions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAtFairValueAdditions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtFairValueAdditions" xlink:to="lab_us-gaap_ServicingAssetAtFairValueAdditions" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpenseImpairmentLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpenseImpairmentLosses"/>
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    <link:label id="lab_us-gaap_ExtendedMaturityMember_4ca657db-685c-46e7-adef-bce7d295ad0f_terseLabel_en-US" xlink:label="lab_us-gaap_ExtendedMaturityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term Extension</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_48cfa516-54c5-4b53-928a-889102b1213e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: imputed interest</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_291a8d87-a00c-47be-8067-18f84005e88b_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_f6997153-5b78-4856-bc93-e302569f1832_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total lease payments</link:label>
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    <link:label id="lab_us-gaap_OtherCommitmentsDomain_60a84b0a-c8b7-4bd7-87e8-fbfc321aff78_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Domain]</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsDomain_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentsDomain"/>
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    <link:label id="lab_us-gaap_VariableInterestEntityOwnershipPercentage_553dfd0c-e27d-4a0f-ba72-6c10ada33b66_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">VIE ownership percentage</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityOwnershipPercentage_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Qualitative or Quantitative Information, Ownership Percentage</link:label>
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    <link:label id="lab_srt_FinancingReceivableAllowanceForCreditLossToOutstandingPercent_2b4f3145-bfbc-4bfe-b2f9-6be6b20556db_terseLabel_en-US" xlink:label="lab_srt_FinancingReceivableAllowanceForCreditLossToOutstandingPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit loss to loans held for investment ratio</link:label>
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    <link:label id="lab_fbc_OtherLoansHeldForInvestmentMember_b8000439-5158-4358-9943-39fd7854ec62_terseLabel_en-US" xlink:label="lab_fbc_OtherLoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial and industrial</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_957a6b64-8f78-4355-a513-e4051f89408b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Components</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_77e3b56b-8848-4b1e-b556-191c7c084497_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-Average Grant Date Fair Value</link:label>
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    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilities"/>
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    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeDomain_e5f04dd2-b70e-41f3-8205-d8f181148afb_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeDomain"/>
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    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
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    <link:label id="lab_us-gaap_LoanRestructuringModificationAxis_699487c3-cd64-4c20-bee8-bc6e26e1b843_terseLabel_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Axis]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:to="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalAbstract_016edd09-9af7-4a66-9adc-03cc085d13a5_terseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leverage Capital</link:label>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Leverage Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneLeverageCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneLeverageCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TierOneLeverageCapitalAbstract" xlink:to="lab_us-gaap_TierOneLeverageCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_4dac81b4-d34b-41d4-8be3-d4212129eadc_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures_0aeb52b7-d3ba-41c7-90c7-3c079e94ced6_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares issued for restricted stock, net of forfeitures</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Restricted Stock Award, Net of Forfeitures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_02e86852-d2cf-49c7-9a58-558fd14269d9_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember_2c325403-7207-48e9-89da-7f44c0d40bca_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of actuarial losses</link:label>
    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Defined Benefit Plans Adjustment, Net Gain (Loss) Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:to="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsumerPortfolioSegmentMember_1666ab8e-7053-4263-8ad2-5602b64a138c_terseLabel_en-US" xlink:label="lab_us-gaap_ConsumerPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consumer and other</link:label>
    <link:label id="lab_us-gaap_ConsumerPortfolioSegmentMember_label_en-US" xlink:label="lab_us-gaap_ConsumerPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consumer Portfolio Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsumerPortfolioSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsumerPortfolioSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsumerPortfolioSegmentMember" xlink:to="lab_us-gaap_ConsumerPortfolioSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_BankingRegulationTier1LeverageCapitalExcessRatio_431322ee-e309-42d9-9552-5563e6a02826_terseLabel_en-US" xlink:label="lab_fbc_BankingRegulationTier1LeverageCapitalExcessRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excess, ratio</link:label>
    <link:label id="lab_fbc_BankingRegulationTier1LeverageCapitalExcessRatio_label_en-US" xlink:label="lab_fbc_BankingRegulationTier1LeverageCapitalExcessRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Leverage Capital, Excess Ratio</link:label>
    <link:label id="lab_fbc_BankingRegulationTier1LeverageCapitalExcessRatio_documentation_en-US" xlink:label="lab_fbc_BankingRegulationTier1LeverageCapitalExcessRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Leverage Capital, Excess Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_BankingRegulationTier1LeverageCapitalExcessRatio" xlink:href="fbc-20251231.xsd#fbc_BankingRegulationTier1LeverageCapitalExcessRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_BankingRegulationTier1LeverageCapitalExcessRatio" xlink:to="lab_fbc_BankingRegulationTier1LeverageCapitalExcessRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_fc084f67-3510-4ca6-863f-cfa3dc247de4_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reclassification out of Accumulated Other Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:to="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTableTextBlock"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeAbstract_4765295c-3211-4661-89cd-5d62db86d97d_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes recognized in other comprehensive income (loss) for the year ended December 31:</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Amounts Recognized in Other Comprehensive Income (Loss) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeAbstract"/>
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    <link:label id="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables_4a709858-f714-41dd-9e20-80446295ba12_negatedLabel_en-US" xlink:label="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other changes in loans, net</link:label>
    <link:label id="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables_label_en-US" xlink:label="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments For (Proceeds From) Other Changes In Financing Receivables</link:label>
    <link:label id="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables_documentation_en-US" xlink:label="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments For (Proceeds From) Other Changes In Financing Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables" xlink:href="fbc-20251231.xsd#fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables" xlink:to="lab_fbc_PaymentsForProceedsFromOtherChangesInFinancingReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalAbstract_1d0b856b-b850-480b-8e90-cd69d9d32a22_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_CapitalAbstract_label_en-US" xlink:label="lab_us-gaap_CapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalAbstract" xlink:to="lab_us-gaap_CapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
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    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_019c656e-a1bf-7b83-a1ca-bb86e36acf90_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expense</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfFinancingCosts"/>
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    <link:label id="lab_us-gaap_ScheduleOfImpairedFinancingReceivableTable_360d409c-f12c-42cb-b181-4502a4279e53_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfImpairedFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Impaired Financing Receivable [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfImpairedFinancingReceivableTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfImpairedFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Impaired Financing Receivable [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfImpairedFinancingReceivableTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfImpairedFinancingReceivableTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfImpairedFinancingReceivableTable" xlink:to="lab_us-gaap_ScheduleOfImpairedFinancingReceivableTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_9a8378e0-19fc-415a-844c-044bde67dfb9_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCredits_019c4d6b-ab06-75f5-868d-3b4d4ed8e66d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCredits" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Federal tax credits</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCredits_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCredits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Credit, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCredits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTaxCredits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCredits" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCredits" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivableOther_019c2477-c31d-72ef-b46a-6809244498db_negatedLabel_en-US" xlink:label="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivableOther" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: other</link:label>
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    <link:label id="lab_us-gaap_CommonStockSharesIssued_97b886e3-76d4-4470-bb53-0f66f5524a0e_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
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    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_9bc6bf36-ecdd-49bf-a37d-9212dcbdc2b4_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average remaining lease term</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
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    <link:label id="lab_fbc_SeriesDPreferredStockWarrantsMember_9e2df512-3607-46a9-84e6-4b942c94f080_terseLabel_en-US" xlink:label="lab_fbc_SeriesDPreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series D Preferred Stock Warrants</link:label>
    <link:label id="lab_fbc_SeriesDPreferredStockWarrantsMember_label_en-US" xlink:label="lab_fbc_SeriesDPreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series D Preferred Stock Warrants [Member]</link:label>
    <link:label id="lab_fbc_SeriesDPreferredStockWarrantsMember_documentation_en-US" xlink:label="lab_fbc_SeriesDPreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series D Preferred Stock Warrants</link:label>
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    <link:label id="lab_us-gaap_TransferOfPortfolioLoansAndLeasesToHeldForSale1_5dad8029-521a-4eb3-bade-6cc22945329c_terseLabel_en-US" xlink:label="lab_us-gaap_TransferOfPortfolioLoansAndLeasesToHeldForSale1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfer of loans from held for investment to held for sale</link:label>
    <link:label id="lab_us-gaap_TransferOfPortfolioLoansAndLeasesToHeldForSale1_label_en-US" xlink:label="lab_us-gaap_TransferOfPortfolioLoansAndLeasesToHeldForSale1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan and Lease, Transfer from Held-in-Portfolio to Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferOfPortfolioLoansAndLeasesToHeldForSale1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransferOfPortfolioLoansAndLeasesToHeldForSale1"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterestAllowanceForCreditLossSecuritiesSold_d9f4bb53-d230-4649-83c0-f7df4669c78f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterestAllowanceForCreditLossSecuritiesSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale securities sold</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterestAllowanceForCreditLossSecuritiesSold_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterestAllowanceForCreditLossSecuritiesSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Excluding Accrued Interest, Allowance for Credit Loss, Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterestAllowanceForCreditLossSecuritiesSold" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterestAllowanceForCreditLossSecuritiesSold"/>
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    <link:label id="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_fff2433f-5cb9-490e-b74e-3571d4b43994_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GSE certificates</link:label>
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    <link:label id="lab_dei_EntityPublicFloat_186df976-234e-48b2-a102-a8138cb00805_terseLabel_en-US" xlink:label="lab_dei_EntityPublicFloat" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Public Float</link:label>
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    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanAccumulatedOtherComprehensiveIncomeNetGainsLossesBeforeTax_45a40f39-b654-49bb-b30e-8f484bf08c96_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAccumulatedOtherComprehensiveIncomeNetGainsLossesBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Actuarial loss, net</link:label>
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    <link:label id="lab_fbc_FlagstarStatutoryTrustXMember_7a6a9816-4062-48c6-ab2b-626cf825c88f_terseLabel_en-US" xlink:label="lab_fbc_FlagstarStatutoryTrustXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Flagstar Statutory Trust X</link:label>
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    <link:label id="lab_fbc_LoansAndLeasesMember_6a734952-a4e0-43dd-8208-e28cb7ee97d9_terseLabel_en-US" xlink:label="lab_fbc_LoansAndLeasesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans and leases held-for-investment</link:label>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_3dc2fb31-142a-4907-86d9-75e50998fc88_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in cash, cash equivalents, and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAmountRollForward_81346b2b-3c0e-40ea-acfb-1a522f5c23ef_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAmountRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing Asset at Fair Value [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAmountRollForward_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAmountRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Fair Value, Amount [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtFairValueAmountRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAtFairValueAmountRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtFairValueAmountRollForward" xlink:to="lab_us-gaap_ServicingAssetAtFairValueAmountRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_1131b49c-9d92-46cf-85a4-4b43b02b47ad_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_FinancingReceivableAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_d4eb8098-d539-4558-b24e-726ff53e5ec6_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dilutive potential common shares (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted, Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:to="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesGainLoss_019c5871-9e66-73ae-bdcb-1edf28ea14e4_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain - net gain on investment securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesGainLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesGainLoss" xlink:to="lab_us-gaap_DebtSecuritiesGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_DefinedBenefitPlanEquityLargeCapValueMember_e1af9b3b-ec68-4ab4-80f1-593127adaa46_terseLabel_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquityLargeCapValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Large-cap value</link:label>
    <link:label id="lab_fbc_DefinedBenefitPlanEquityLargeCapValueMember_label_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquityLargeCapValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Equity, Large Cap Value [Member]</link:label>
    <link:label id="lab_fbc_DefinedBenefitPlanEquityLargeCapValueMember_documentation_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquityLargeCapValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Equity, Large Cap Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_DefinedBenefitPlanEquityLargeCapValueMember" xlink:href="fbc-20251231.xsd#fbc_DefinedBenefitPlanEquityLargeCapValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_DefinedBenefitPlanEquityLargeCapValueMember" xlink:to="lab_fbc_DefinedBenefitPlanEquityLargeCapValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_ba416bc9-3e16-4969-a4e9-058053dd2efb_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on common stock (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Cash Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockDividendsPerShareCashPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:to="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_LoansHeldForInvestmentMember_ba11abf2-6982-44db-a7de-d9d85aa9aa7e_terseLabel_en-US" xlink:label="lab_fbc_LoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held-for-investment</link:label>
    <link:label id="lab_fbc_LoansHeldForInvestmentMember_label_en-US" xlink:label="lab_fbc_LoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Held-For-Investment [Member]</link:label>
    <link:label id="lab_fbc_LoansHeldForInvestmentMember_documentation_en-US" xlink:label="lab_fbc_LoansHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans Held-For-Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_LoansHeldForInvestmentMember" xlink:href="fbc-20251231.xsd#fbc_LoansHeldForInvestmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_LoansHeldForInvestmentMember" xlink:to="lab_fbc_LoansHeldForInvestmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_21bb93bb-3985-4242-84e2-8bac30e3a914_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_f809c306-da7a-44b7-8132-9243b4ccba21_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationsAbstract_85636dce-b821-40e8-9cfd-644e5d09277c_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combinations:</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationsAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationsAbstract" xlink:to="lab_us-gaap_BusinessCombinationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_LoanAdministrationIncomeExpense_822e0514-cb4b-4bcd-9409-1e59ef3fde1e_verboseLabel_en-US" xlink:label="lab_fbc_LoanAdministrationIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net loan administration income</link:label>
    <link:label id="lab_fbc_LoanAdministrationIncomeExpense_label_en-US" xlink:label="lab_fbc_LoanAdministrationIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Administration Income (Expense)</link:label>
    <link:label id="lab_fbc_LoanAdministrationIncomeExpense_documentation_en-US" xlink:label="lab_fbc_LoanAdministrationIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan Administration Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_LoanAdministrationIncomeExpense" xlink:href="fbc-20251231.xsd#fbc_LoanAdministrationIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_LoanAdministrationIncomeExpense" xlink:to="lab_fbc_LoanAdministrationIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_ef7cbcf8-4d33-4614-a767-114e90694684_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_TemporaryEquityStockIssuedDuringPeriodShareNewIssues_2c7d386c-bd3a-4d2d-abe7-4083e6c38b77_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquityStockIssuedDuringPeriodShareNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of mezzanine preferred stock Series , net (in shares)</link:label>
    <link:label id="lab_fbc_TemporaryEquityStockIssuedDuringPeriodShareNewIssues_label_en-US" xlink:label="lab_fbc_TemporaryEquityStockIssuedDuringPeriodShareNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Stock Issued During Period, Share, New Issues</link:label>
    <link:label id="lab_fbc_TemporaryEquityStockIssuedDuringPeriodShareNewIssues_documentation_en-US" xlink:label="lab_fbc_TemporaryEquityStockIssuedDuringPeriodShareNewIssues" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Stock Issued During Period, Share, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_TemporaryEquityStockIssuedDuringPeriodShareNewIssues" xlink:href="fbc-20251231.xsd#fbc_TemporaryEquityStockIssuedDuringPeriodShareNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_TemporaryEquityStockIssuedDuringPeriodShareNewIssues" xlink:to="lab_fbc_TemporaryEquityStockIssuedDuringPeriodShareNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityAbstract_871fde7b-2a70-4d27-af5c-79123e612ce1_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mezzanine equity:</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityAbstract_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityAbstract" xlink:to="lab_us-gaap_TemporaryEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_FinancingReceivablePurchasedWithCreditDeteriorationTableTextBlock_73b3c9b1-3a67-4b96-a9aa-6d5ff34e3f3e_terseLabel_en-US" xlink:label="lab_fbc_FinancingReceivablePurchasedWithCreditDeteriorationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Loans and Leases Purchased as Part of Acquisition</link:label>
    <link:label id="lab_fbc_FinancingReceivablePurchasedWithCreditDeteriorationTableTextBlock_label_en-US" xlink:label="lab_fbc_FinancingReceivablePurchasedWithCreditDeteriorationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Purchased With Credit Deterioration [Table Text Block]</link:label>
    <link:label id="lab_fbc_FinancingReceivablePurchasedWithCreditDeteriorationTableTextBlock_documentation_en-US" xlink:label="lab_fbc_FinancingReceivablePurchasedWithCreditDeteriorationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Purchased With Credit Deterioration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FinancingReceivablePurchasedWithCreditDeteriorationTableTextBlock" xlink:href="fbc-20251231.xsd#fbc_FinancingReceivablePurchasedWithCreditDeteriorationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_FinancingReceivablePurchasedWithCreditDeteriorationTableTextBlock" xlink:to="lab_fbc_FinancingReceivablePurchasedWithCreditDeteriorationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome_019b8ef6-6830-7890-b292-38c638fdb63b_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income recognized on non-accrual loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Nonaccrual, Interest Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableNonaccrualInterestIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableNonaccrualInterestIncome"/>
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    <link:label id="lab_fbc_PrivateLabelCMOsMember_3f1be4f5-1576-4955-be85-ecb9f6f6f546_terseLabel_en-US" xlink:label="lab_fbc_PrivateLabelCMOsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Label CMOs</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfServicingAssetsAtFairValueTextBlock_0ca7128a-1c81-40c6-ad58-d461a579176c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfServicingAssetsAtFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in the Fair Value of Residential First Mortgage MSRs</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_1fa7cb51-0b70-4a8a-abee-3617fd277655_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combinations</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Text Block]</link:label>
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    <link:label id="lab_us-gaap_LongTermDebtWeightedAverageInterestRateOverTime_019c2490-b89f-71fa-9ff3-58e876404952_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtWeightedAverageInterestRateOverTime" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average interest rate on long-term debt</link:label>
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    <link:label id="lab_us-gaap_SharesSubjectToMandatoryRedemptionSettlementTermsFairValueOfShares_bfde856b-0df4-4db3-8737-4998b0656c52_terseLabel_en-US" xlink:label="lab_us-gaap_SharesSubjectToMandatoryRedemptionSettlementTermsFairValueOfShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Settlement terms, fair value of shares amount</link:label>
    <link:label id="lab_us-gaap_SharesSubjectToMandatoryRedemptionSettlementTermsFairValueOfShares_label_en-US" xlink:label="lab_us-gaap_SharesSubjectToMandatoryRedemptionSettlementTermsFairValueOfShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments Subject to Mandatory Redemption, Settlement Terms, Fair Value of Shares</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedSubsequentDefault_580e7c49-a35a-47bb-8f9f-bf844426f550_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedSubsequentDefault" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:label id="lab_fbc_ProceedsFromSaleOfDebtSecuritiesAvailableForSaleAndSecuritizedLoans_481ebf97-074f-4107-a1ee-93b9f495272f_terseLabel_en-US" xlink:label="lab_fbc_ProceedsFromSaleOfDebtSecuritiesAvailableForSaleAndSecuritizedLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sales of securities available-for-sale including loans that have been securitized</link:label>
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    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_1c4df0c6-35af-49b7-b12c-61b30ff9c750_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill impairment</link:label>
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    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Impairment Loss</link:label>
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    <link:label id="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock_85cf1f74-d78f-4c99-9036-f0b3b101c2c2_terseLabel_en-US" xlink:label="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_ddcefc75-99f9-435e-95c8-723275534435_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated year three</link:label>
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    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_6dc0cddb-9e55-4278-947f-a70c42fe741c_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_ced5930a-ffd8-46be-9402-f21b02654973_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
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    <link:label id="lab_us-gaap_ConsumerOtherMember_019c4b79-b809-79cf-8e0a-b98337ad5fb8_terseLabel_en-US" xlink:label="lab_us-gaap_ConsumerOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Consumer</link:label>
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    <link:label id="lab_fbc_SeriesDNYCEStockMember_documentation_en-US" xlink:label="lab_fbc_SeriesDNYCEStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series D NYCE Stock</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_ad316d5e-e8d7-42b2-a7a9-80c103635b1a_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:to="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment_8c866792-4e5c-4c18-bb7c-6a1c72c7a168_negatedTerseLabel_en-US" xlink:label="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: purchase accounting adjustment</link:label>
    <link:label id="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment_label_en-US" xlink:label="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type And Direct Financing Leases, Lease Receivable, Purchase Accounting Adjustment</link:label>
    <link:label id="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment_documentation_en-US" xlink:label="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sales-Type And Direct Financing Leases, Lease Receivable, Purchase Accounting Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment" xlink:href="fbc-20251231.xsd#fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment" xlink:to="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivablePurchaseAccountingAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_474b3b64-fdaf-4870-bb97-b1f401af0f1d_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CASH FLOWS FROM OPERATING ACTIVITIES:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_b74c2910-30c1-4c48-bf14-1a4337a8c4bb_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated useful life</link:label>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_label_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquired Finite-Lived Intangible Assets, Weighted Average Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:to="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorDirectFinancingLeaseTermOfContract1_54a75d0c-0473-4a56-8d51-d67e239c8f73_terseLabel_en-US" xlink:label="lab_us-gaap_LessorDirectFinancingLeaseTermOfContract1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term of lease</link:label>
    <link:label id="lab_us-gaap_LessorDirectFinancingLeaseTermOfContract1_label_en-US" xlink:label="lab_us-gaap_LessorDirectFinancingLeaseTermOfContract1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Direct Financing Lease, Term of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorDirectFinancingLeaseTermOfContract1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorDirectFinancingLeaseTermOfContract1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorDirectFinancingLeaseTermOfContract1" xlink:to="lab_us-gaap_LessorDirectFinancingLeaseTermOfContract1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseBorrowings_019c4b94-9075-70c4-a786-6720c64dbd56_totalLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseBorrowings" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseBorrowings_label_en-US" xlink:label="lab_us-gaap_InterestExpenseBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Borrowings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseBorrowings" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseBorrowings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseBorrowings" xlink:to="lab_us-gaap_InterestExpenseBorrowings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_da316e05-80ee-4350-8256-eab704b75e77_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_DefinedBenefitPlanEquityNonUSGrowthMember_49cdfb1c-0e34-4210-9eb2-3a31a5151829_terseLabel_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquityNonUSGrowthMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">International growth</link:label>
    <link:label id="lab_fbc_DefinedBenefitPlanEquityNonUSGrowthMember_label_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquityNonUSGrowthMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Equity, Non-US, Growth [Member]</link:label>
    <link:label id="lab_fbc_DefinedBenefitPlanEquityNonUSGrowthMember_documentation_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquityNonUSGrowthMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Equity, Non-US, Growth</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_DefinedBenefitPlanEquityNonUSGrowthMember" xlink:href="fbc-20251231.xsd#fbc_DefinedBenefitPlanEquityNonUSGrowthMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_DefinedBenefitPlanEquityNonUSGrowthMember" xlink:to="lab_fbc_DefinedBenefitPlanEquityNonUSGrowthMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_052ea02f-d586-4390-8463-ee01894c858e_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets_154e55f9-4d13-4083-80a4-0976ce0f113d_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum for capital adequacy, ratio</link:label>
    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets_label_en-US" xlink:label="lab_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital Ratio, Capital Adequacy, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:to="lab_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseSavingsDeposits_1e455739-c15d-41b7-97b8-716b473609ea_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseSavingsDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Savings accounts</link:label>
    <link:label id="lab_us-gaap_InterestExpenseSavingsDeposits_label_en-US" xlink:label="lab_us-gaap_InterestExpenseSavingsDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Savings Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseSavingsDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseSavingsDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseSavingsDeposits" xlink:to="lab_us-gaap_InterestExpenseSavingsDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_eec66303-377b-4595-b0a3-27cd888f2e96_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_28c07256-053b-4bef-b874-d6e3185ae831_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:to="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_e52f1687-4fec-4929-8aca-b817a54b62f0_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets acquired</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_afb20766-b202-4070-ad6c-8dfe56feb6a3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Other Observable Inputs (Level 2)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFinStmtErrorCorrectionFlag_2a98f592-9be8-493c-a27e-bebcfe06c958_terseLabel_en-US" xlink:label="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Financial Statement Error Correction [Flag]</link:label>
    <link:label id="lab_dei_DocumentFinStmtErrorCorrectionFlag_label_en-US" xlink:label="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Financial Statement Error Correction [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFinStmtErrorCorrectionFlag" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFinStmtErrorCorrectionFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFinStmtErrorCorrectionFlag" xlink:to="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_11a6dcf8-faf1-479a-b521-e7bda5af2244_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State and local income taxes, net of federal income tax effect</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, State and Local Income Taxes, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes"/>
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    <link:label id="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare_a8fae5e3-e3aa-491d-b6d9-fb56bc4935bf_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncumulative convertible preferred stock (in usd per share)</link:label>
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    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_5010ee6c-03c5-48f8-888f-5dc95e6d3f27_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetPledgedAsCollateralMember_4d5d19c0-6dae-4f59-b152-9084d7b25a09_terseLabel_en-US" xlink:label="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset pledged as collateral</link:label>
    <link:label id="lab_us-gaap_AssetPledgedAsCollateralMember_label_en-US" xlink:label="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Pledged as Collateral [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetPledgedAsCollateralMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetPledgedAsCollateralMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetPledgedAsCollateralMember" xlink:to="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember_6cfcde37-7eaa-4b09-b8f6-0cf90b6bfb95_terseLabel_en-US" xlink:label="lab_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed-to-Floating Rate Series A Noncumulative Perpetual Preferred Stock</link:label>
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    <link:label id="lab_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember_documentation_en-US" xlink:label="lab_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed-to-Floating Rate Series A Noncumulative Perpetual Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember" xlink:href="fbc-20251231.xsd#fbc_FixedToFloatingRateSeriesANoncumulativePerpetualPreferredStockMember"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanChangeInFairValueOfPlanAssetsRollForward_ec6abf97-d8ad-4049-8a03-14bdbb3fd3e0_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanChangeInFairValueOfPlanAssetsRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Plan Assets:</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanChangeInFairValueOfPlanAssetsRollForward_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanChangeInFairValueOfPlanAssetsRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Change in Fair Value of Plan Assets [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanChangeInFairValueOfPlanAssetsRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanChangeInFairValueOfPlanAssetsRollForward"/>
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    <link:label id="lab_us-gaap_ResidentialMortgageMember_72db53a6-b7d1-4378-9ccc-42ca76360ad7_terseLabel_en-US" xlink:label="lab_us-gaap_ResidentialMortgageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential first mortgage loans</link:label>
    <link:label id="lab_us-gaap_ResidentialMortgageMember_label_en-US" xlink:label="lab_us-gaap_ResidentialMortgageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResidentialMortgageMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ResidentialMortgageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResidentialMortgageMember" xlink:to="lab_us-gaap_ResidentialMortgageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_5316c3f0-41f7-4287-a906-8152851daed2_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Components of the Provision (Benefit) for Income Taxes</link:label>
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    <link:label id="lab_fbc_ProfessionalServices_019be98a-b608-7cc3-a918-e99fc8148147_terseLabel_en-US" xlink:label="lab_fbc_ProfessionalServices" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Professional services</link:label>
    <link:label id="lab_fbc_ProfessionalServices_label_en-US" xlink:label="lab_fbc_ProfessionalServices" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Professional Services</link:label>
    <link:label id="lab_fbc_ProfessionalServices_documentation_en-US" xlink:label="lab_fbc_ProfessionalServices" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Professional Services</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_ProfessionalServices" xlink:href="fbc-20251231.xsd#fbc_ProfessionalServices"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_992223b2-8132-4dda-9694-68da4aaca9c7_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premises and Equipment, Net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedFiveYears_14681073-290b-4276-a0f8-2310f400390f_terseLabel_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedFiveYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
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    <link:label id="lab_dei_DocumentInformationTable_0ad550fb-e46b-468f-b953-2736aeb4deaf_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
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    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoMember"/>
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    <link:label id="lab_us-gaap_TierOneLeverageCapital_01adfd50-5cdd-4d76-9c1f-694be15bb10e_terseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total capital, amount</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_45ffcf44-bf76-4600-8ae2-48403d239024_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Axis]</link:label>
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    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_496d2282-6272-42c5-9f57-6c3d8bf0b214_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Payment Arrangement [Abstract]</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_aa0053e0-e4f6-47d0-89a3-5a3a0be41509_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents, and restricted cash at beginning of year</link:label>
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    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
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    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
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    <link:label id="lab_us-gaap_PreferredStockDividendsPerShareCashPaid_46b9a409-683a-4f6f-8b1c-30f99d6edfcb_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on preferred stock (in dollars per share)</link:label>
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    <link:label id="lab_dei_CityAreaCode_10e47afd-6449-40f3-bc3c-e947983eb8c7_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
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    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_3c1bb513-4abd-48cb-9e5c-69d22d90d414_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Additional Information about Nonaccrual Loans</link:label>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanPlanAssetsCategoryLineItems_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanPlanAssetsCategoryLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Plan Assets, Category [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanPlanAssetsCategoryLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanPlanAssetsCategoryLineItems"/>
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    <link:label id="lab_us-gaap_JuniorSubordinatedDebentureOwedToUnconsolidatedSubsidiaryTrust_c4af98a3-4770-41cb-ab4a-c798522a2d1e_terseLabel_en-US" xlink:label="lab_us-gaap_JuniorSubordinatedDebentureOwedToUnconsolidatedSubsidiaryTrust" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Junior subordinated debentures</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_46f66798-d3ea-4143-9a33-7d88012a54f7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, and Equity Securities, FV-NI [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, and Equity Securities, FV-NI [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable"/>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilities_85c88f8c-a7d4-4209-b023-ef7beab871be_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net deferred tax liability</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Net</link:label>
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    <link:label id="lab_fbc_NoncumulativePreferredStockSeriesBMember_93b465f0-ffc7-411b-9308-3fe8b3d03b7e_terseLabel_en-US" xlink:label="lab_fbc_NoncumulativePreferredStockSeriesBMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncumulative Preferred Stock Series B</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_49fa9edf-4d5f-4c02-8f11-bf2d742c4554_verboseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">CASH FLOWS FROM INVESTING ACTIVITIES:</link:label>
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    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_61ab6a65-ef40-4b3a-a259-ae5ad5ab765e_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_be7ee8ba-2160-4d90-b724-f18a41d8d3a0_verboseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">General and administrative</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
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    <link:label id="lab_fbc_FairValueOptionContractualPrincipalOutstandingAssets_db8e8263-dc54-4c2a-a4a3-33620aee4488_terseLabel_en-US" xlink:label="lab_fbc_FairValueOptionContractualPrincipalOutstandingAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unpaid Principal Balance</link:label>
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    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_6d37931c-8e44-489d-91c6-6cd28765cd51_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible List]</link:label>
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    <link:label id="lab_us-gaap_FairValueHedgingMember_51cbdbeb-8086-40f8-ae88-cda1e292fea6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueHedgingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value hedging</link:label>
    <link:label id="lab_us-gaap_FairValueHedgingMember_label_en-US" xlink:label="lab_us-gaap_FairValueHedgingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hedging [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanEquitySecuritiesNonUsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanEquitySecuritiesNonUsMember"/>
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    <link:label id="lab_us-gaap_BuildingMember_63481ff1-54d0-455e-ace6-c5af814d8e33_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Buildings</link:label>
    <link:label id="lab_us-gaap_BuildingMember_label_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building [Member]</link:label>
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    <link:label id="lab_us-gaap_DebtAndEquitySecuritiesGainLoss_fb29578a-ed4f-46bb-a581-e875e670bbbc_terseLabel_en-US" xlink:label="lab_us-gaap_DebtAndEquitySecuritiesGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gain on investment securities</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtAndEquitySecuritiesGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtAndEquitySecuritiesGainLoss"/>
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    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Policy [Policy Text Block]</link:label>
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    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Disclosure [Text Block]</link:label>
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    <link:label id="lab_us-gaap_NondesignatedMember_56067c17-d0f2-4c0f-9a23-eb55d985d996_terseLabel_en-US" xlink:label="lab_us-gaap_NondesignatedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives not designated as hedging instruments:</link:label>
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    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_dd5f4f84-0179-4cc5-9fdc-01e9caedc8a2_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U. S. Treasury obligations</link:label>
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    <link:label id="lab_fbc_DebtSecuritiesAvailableForSaleMember_b6754a82-1a57-4ee2-bd58-ade882712702_terseLabel_en-US" xlink:label="lab_fbc_DebtSecuritiesAvailableForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt securities available-for-sale</link:label>
    <link:label id="lab_fbc_DebtSecuritiesAvailableForSaleMember_label_en-US" xlink:label="lab_fbc_DebtSecuritiesAvailableForSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available for Sale [Member]</link:label>
    <link:label id="lab_fbc_DebtSecuritiesAvailableForSaleMember_documentation_en-US" xlink:label="lab_fbc_DebtSecuritiesAvailableForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available for Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_DebtSecuritiesAvailableForSaleMember" xlink:href="fbc-20251231.xsd#fbc_DebtSecuritiesAvailableForSaleMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfNetBenefitCostsTableTextBlock_460893d9-98d8-401e-bc97-fcd339aec9e3_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfNetBenefitCostsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Benefit Costs</link:label>
    <link:label id="lab_us-gaap_ScheduleOfNetBenefitCostsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfNetBenefitCostsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Net Benefit Costs [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfNetBenefitCostsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfNetBenefitCostsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfNetBenefitCostsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfNetBenefitCostsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentsTableTextBlock_96ae32f7-2724-43ec-ad31-90db7483b1ed_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of the Contractual Amount of Significant Commitments</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsTableTextBlock" xlink:to="lab_us-gaap_OtherCommitmentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
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    <link:label id="lab_us-gaap_ComprehensiveIncomeNoteTextBlock_a1c2572f-2603-4020-9053-581c3f536290_terseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNoteTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Loss</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNoteTextBlock_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNoteTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss) Note [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNoteTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNoteTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNoteTextBlock" xlink:to="lab_us-gaap_ComprehensiveIncomeNoteTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_69fdedd9-9c88-4797-94e3-71a2e87077dc_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
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    <link:label id="lab_fbc_FinancingReceivableWithNoRelatedAllowanceAverageRecordedInvestment_3413ae71-06fa-487d-807a-3f0b3742cdd3_terseLabel_en-US" xlink:label="lab_fbc_FinancingReceivableWithNoRelatedAllowanceAverageRecordedInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-accrual loans with no related allowance:</link:label>
    <link:label id="lab_fbc_FinancingReceivableWithNoRelatedAllowanceAverageRecordedInvestment_label_en-US" xlink:label="lab_fbc_FinancingReceivableWithNoRelatedAllowanceAverageRecordedInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, With No Related Allowance, Average Recorded Investment</link:label>
    <link:label id="lab_fbc_FinancingReceivableWithNoRelatedAllowanceAverageRecordedInvestment_documentation_en-US" xlink:label="lab_fbc_FinancingReceivableWithNoRelatedAllowanceAverageRecordedInvestment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, With No Related Allowance, Average Recorded Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FinancingReceivableWithNoRelatedAllowanceAverageRecordedInvestment" xlink:href="fbc-20251231.xsd#fbc_FinancingReceivableWithNoRelatedAllowanceAverageRecordedInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_FinancingReceivableWithNoRelatedAllowanceAverageRecordedInvestment" xlink:to="lab_fbc_FinancingReceivableWithNoRelatedAllowanceAverageRecordedInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_48ec0f5d-a8f2-4c5d-8ce1-6740e366f282_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee Arrangements</link:label>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Leases [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeasesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:to="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_356f3028-2b23-4b34-8aa4-0f5d1e0b1917_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible asset amortization</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_e2b8079e-3f85-4aa9-8d93-890a8249c870_netLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Amortization expense</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Intangible Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:to="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_CommonStockLiquidationPreferenceValue_17fcdd7f-cf6a-4e9f-9c2f-56df1c8770cc_terseLabel_en-US" xlink:label="lab_fbc_CommonStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_fbc_CommonStockLiquidationPreferenceValue_label_en-US" xlink:label="lab_fbc_CommonStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Liquidation Preference, Value</link:label>
    <link:label id="lab_fbc_CommonStockLiquidationPreferenceValue_documentation_en-US" xlink:label="lab_fbc_CommonStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Liquidation Preference, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_CommonStockLiquidationPreferenceValue" xlink:href="fbc-20251231.xsd#fbc_CommonStockLiquidationPreferenceValue"/>
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    <link:label id="lab_us-gaap_DirectFinancingLeaseUnguaranteedResidualAsset_3e5f5d7f-fe8c-4535-adb4-260766c3d42c_terseLabel_en-US" xlink:label="lab_us-gaap_DirectFinancingLeaseUnguaranteedResidualAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unguaranteed residual assets</link:label>
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    <link:label id="lab_fbc_SignatureBridgeBankMember_18392fe3-e064-4d0e-9f58-12e9c8145e4f_terseLabel_en-US" xlink:label="lab_fbc_SignatureBridgeBankMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Signature Bridge Bank</link:label>
    <link:label id="lab_fbc_SignatureBridgeBankMember_label_en-US" xlink:label="lab_fbc_SignatureBridgeBankMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Signature Bridge Bank [Member]</link:label>
    <link:label id="lab_fbc_SignatureBridgeBankMember_documentation_en-US" xlink:label="lab_fbc_SignatureBridgeBankMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Signature Bridge Bank</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_SignatureBridgeBankMember" xlink:href="fbc-20251231.xsd#fbc_SignatureBridgeBankMember"/>
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    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_e2997105-bd1f-44f6-815f-0dacd8823422_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of common stock</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Value</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_80ff7e7f-539f-499e-98df-3f241e68df2d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in Accumulated Other Comprehensive Income (Loss) by Component, Net of Tax</link:label>
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    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_019c587b-7765-7f68-b12d-735e3d61c831_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
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    <link:label id="lab_fbc_NumberOfLocations_2d57ceaf-239c-4f1d-977f-acfd0a3e6b52_terseLabel_en-US" xlink:label="lab_fbc_NumberOfLocations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of locations</link:label>
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    <link:label id="lab_fbc_NumberOfLocations_documentation_en-US" xlink:label="lab_fbc_NumberOfLocations" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Locations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NumberOfLocations" xlink:href="fbc-20251231.xsd#fbc_NumberOfLocations"/>
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    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrDuration"/>
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    <link:label id="lab_us-gaap_ExcessTierOneRiskBasedCapital_7e1ad8c7-b915-45e9-a6e6-95881797a269_terseLabel_en-US" xlink:label="lab_us-gaap_ExcessTierOneRiskBasedCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excess, amount</link:label>
    <link:label id="lab_us-gaap_ExcessTierOneRiskBasedCapital_label_en-US" xlink:label="lab_us-gaap_ExcessTierOneRiskBasedCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Risk-Based Capital, Excess, Actual</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_d159d8f3-af12-41c5-95da-4d9d2140e8e7_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate of Capital Securities and Debentures</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
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    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_ee273ea5-5ac9-4a3a-bcc2-60d01136fede_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, before Offset</link:label>
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    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_f15d13ba-db88-4689-853b-0271b43bf0af_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncumulative convertible preferred stock (in shares)</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost_5aef90b9-a35a-4a84-a4fa-f856172a28ea_totalLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net periodic pension (income)</link:label>
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    <link:label id="lab_us-gaap_MunicipalBondsMember_34f13af3-fb7c-437c-88a3-c2ee2dd8fa3a_terseLabel_en-US" xlink:label="lab_us-gaap_MunicipalBondsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Municipal bonds</link:label>
    <link:label id="lab_us-gaap_MunicipalBondsMember_label_en-US" xlink:label="lab_us-gaap_MunicipalBondsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Municipal Bonds [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MunicipalBondsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MunicipalBondsMember"/>
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    <link:label id="lab_fbc_LongIntermediateDurationMember_019bea53-743e-7db2-8d82-1a2d9e91d1b6_terseLabel_en-US" xlink:label="lab_fbc_LongIntermediateDurationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long/Intermediate Duration</link:label>
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    <link:label id="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember_019c4be2-0ce7-75ac-9df4-23fcdb0dbfb9_terseLabel_en-US" xlink:label="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember_label_en-US" xlink:label="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">State and Local Tax Jurisdiction, Other [Member]</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions_8f40dd92-2a2d-4f5c-9b80-d16168334458_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Debt Securities</link:label>
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    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAmount_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Fair Value, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtFairValueAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAtFairValueAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtFairValueAmount" xlink:to="lab_us-gaap_ServicingAssetAtFairValueAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_b3411bd0-1153-475b-99ea-dadd46577ad9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanInterestCost_86c5f130-2917-406a-b5f4-ad89cdb1a1ba_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanInterestCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest cost</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanInterestCost_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanInterestCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Interest Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanInterestCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanInterestCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanInterestCost" xlink:to="lab_us-gaap_DefinedBenefitPlanInterestCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_7040d084-eb2d-4443-8743-08f001ff20e7_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Granted (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_04289082-2715-4666-b158-3c7479198085_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_FeeIncomeOtherOperatingIncomeMember_019c24b6-476e-7d48-ac68-7d5780a09960_terseLabel_en-US" xlink:label="lab_fbc_FeeIncomeOtherOperatingIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fee income</link:label>
    <link:label id="lab_fbc_FeeIncomeOtherOperatingIncomeMember_label_en-US" xlink:label="lab_fbc_FeeIncomeOtherOperatingIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fee income, Other Operating Income [Member]</link:label>
    <link:label id="lab_fbc_FeeIncomeOtherOperatingIncomeMember_documentation_en-US" xlink:label="lab_fbc_FeeIncomeOtherOperatingIncomeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fee income, Other Operating Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FeeIncomeOtherOperatingIncomeMember" xlink:href="fbc-20251231.xsd#fbc_FeeIncomeOtherOperatingIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_FeeIncomeOtherOperatingIncomeMember" xlink:to="lab_fbc_FeeIncomeOtherOperatingIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract_22e5fc49-3520-48f9-b43a-77ebbc794459_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liquidation Preference Per Share</link:label>
    <link:label id="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract_label_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity And Equity, Liquidation Preference [Abstract]</link:label>
    <link:label id="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract_documentation_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity And Equity, Liquidation Preference</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract" xlink:href="fbc-20251231.xsd#fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract" xlink:to="lab_fbc_TemporaryEquityAndEquityLiquidationPreferenceAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_NonaccrualLoansMember_8b7a9f84-8a97-4406-98c2-57761ead47da_terseLabel_en-US" xlink:label="lab_fbc_NonaccrualLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-accrual loans:</link:label>
    <link:label id="lab_fbc_NonaccrualLoansMember_label_en-US" xlink:label="lab_fbc_NonaccrualLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonaccrual Loans [Member]</link:label>
    <link:label id="lab_fbc_NonaccrualLoansMember_documentation_en-US" xlink:label="lab_fbc_NonaccrualLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Nonaccrual Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NonaccrualLoansMember" xlink:href="fbc-20251231.xsd#fbc_NonaccrualLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_NonaccrualLoansMember" xlink:to="lab_fbc_NonaccrualLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_CommercialAndIndustrialLoansMember_f74e5a32-8ee0-4d47-bf96-25c4146289b8_terseLabel_en-US" xlink:label="lab_fbc_CommercialAndIndustrialLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial and industrial</link:label>
    <link:label id="lab_fbc_CommercialAndIndustrialLoansMember_label_en-US" xlink:label="lab_fbc_CommercialAndIndustrialLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial And Industrial Loans [Member]</link:label>
    <link:label id="lab_fbc_CommercialAndIndustrialLoansMember_documentation_en-US" xlink:label="lab_fbc_CommercialAndIndustrialLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Portfolio segment of the company's total financing receivables related to commercial and industrial loans, which includes lines of credit to small or middle market businesses for use in normal business operations to finance working capital needs, equipment purchases and expansion projects.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_CommercialAndIndustrialLoansMember" xlink:href="fbc-20251231.xsd#fbc_CommercialAndIndustrialLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_CommercialAndIndustrialLoansMember" xlink:to="lab_fbc_CommercialAndIndustrialLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_e58e7e95-f98a-4b27-a1bc-9454691caf45_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableBargainGainPercent_019c4d6b-8759-7576-a838-f6d4e5b842cc_negatedTerseLabel_en-US" xlink:label="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableBargainGainPercent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Non-taxable or deductible bargain gain</link:label>
    <link:label id="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableBargainGainPercent_label_en-US" xlink:label="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableBargainGainPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Non-Taxable Bargain Gain, Percent</link:label>
    <link:label id="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableBargainGainPercent_documentation_en-US" xlink:label="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableBargainGainPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Non-Taxable Bargain Gain, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableBargainGainPercent" xlink:href="fbc-20251231.xsd#fbc_EffectiveIncomeTaxRateReconciliationNonTaxableBargainGainPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableBargainGainPercent" xlink:to="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableBargainGainPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_efa95ea0-d1fc-496f-bbdf-8673c19b7ac5_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted_dc625ada-acf3-4650-bb01-1627406beaab_totalLabel_en-US" xlink:label="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total commitments</link:label>
    <link:label id="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted_label_en-US" xlink:label="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments And Guarantor Obligations, Maximum Exposure, Undiscounted</link:label>
    <link:label id="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted_documentation_en-US" xlink:label="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Commitments And Guarantor Obligations, Maximum Exposure, Undiscounted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted" xlink:href="fbc-20251231.xsd#fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted" xlink:to="lab_fbc_OtherCommitmentsAndGuarantorObligationsMaximumExposureUndiscounted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy_17d0b272-6190-4e79-aeec-ca5369521f1b_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans Held for Investment and Non-accrual and Past Due Loans and Leases and Charge-off of Uncollectible Loans</link:label>
    <link:label id="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy_label_en-US" xlink:label="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Held-for-Investment [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:to="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_019c6540-1b29-7024-888e-7efa04989bd7_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other financing activities, net</link:label>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from (Payment for) Other Financing Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromPaymentsForOtherFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:to="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember_e58e0304-5e1d-41f9-861a-1d04dbfc5e18_terseLabel_en-US" xlink:label="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New York Community Capital Trust V (BONUSES Units)</link:label>
    <link:label id="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember_label_en-US" xlink:label="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New York Community Capital Trust V (BONUSES Units) [Member]</link:label>
    <link:label id="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember_documentation_en-US" xlink:label="lab_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New York Community Capital Trust V (BONUSES Units)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember" xlink:href="fbc-20251231.xsd#fbc_NewYorkCommunityCapitalTrustVBONUSESUnitsMember"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract_5427a509-5058-4eef-82c0-d09afa4fb82d_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of liabilities assumed:</link:label>
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    <link:label id="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableBargainGain_97f1ae94-d0f2-40f5-bbf1-5031896e906a_negatedTerseLabel_en-US" xlink:label="lab_fbc_EffectiveIncomeTaxRateReconciliationNonTaxableBargainGain" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Non-taxable or deductible bargain gain</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_3c97e647-921b-46ad-87de-976909222c2e_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Non-vested balance at beginning of period (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_b331a908-794a-4602-a92d-1edfdf90b12b_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Non-vested balance at end of period (in usd per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_NetLoanAdministrationIncomeMember_63dfff69-46bf-4692-96ca-48a7ab12efc2_terseLabel_en-US" xlink:label="lab_fbc_NetLoanAdministrationIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan administration income on mortgage loans subserviced</link:label>
    <link:label id="lab_fbc_NetLoanAdministrationIncomeMember_label_en-US" xlink:label="lab_fbc_NetLoanAdministrationIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Loan Administration Income [Member]</link:label>
    <link:label id="lab_fbc_NetLoanAdministrationIncomeMember_documentation_en-US" xlink:label="lab_fbc_NetLoanAdministrationIncomeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the net loan administration income.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NetLoanAdministrationIncomeMember" xlink:href="fbc-20251231.xsd#fbc_NetLoanAdministrationIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_NetLoanAdministrationIncomeMember" xlink:to="lab_fbc_NetLoanAdministrationIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AociLossCashFlowHedgeCumulativeGainLossAfterTax_8e7541db-0ac6-43dd-b0d0-3bc419f71a03_terseLabel_en-US" xlink:label="lab_us-gaap_AociLossCashFlowHedgeCumulativeGainLossAfterTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains on derivatives</link:label>
    <link:label id="lab_us-gaap_AociLossCashFlowHedgeCumulativeGainLossAfterTax_label_en-US" xlink:label="lab_us-gaap_AociLossCashFlowHedgeCumulativeGainLossAfterTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Cash Flow Hedge, Cumulative Gain (Loss), after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AociLossCashFlowHedgeCumulativeGainLossAfterTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AociLossCashFlowHedgeCumulativeGainLossAfterTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AociLossCashFlowHedgeCumulativeGainLossAfterTax" xlink:to="lab_us-gaap_AociLossCashFlowHedgeCumulativeGainLossAfterTax" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember_36f83cde-0d91-4465-b8be-ac24f781f26d_terseLabel_en-US" xlink:label="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other noninterest income</link:label>
    <link:label id="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember_label_en-US" xlink:label="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income, Other Operating Income [Member]</link:label>
    <link:label id="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember_documentation_en-US" xlink:label="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents other forms of revenue earned, excluding interest, which is not otherwise specified in the taxonomy.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NoninterestIncomeOtherOperatingIncomeMember" xlink:href="fbc-20251231.xsd#fbc_NoninterestIncomeOtherOperatingIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_NoninterestIncomeOtherOperatingIncomeMember" xlink:to="lab_fbc_NoninterestIncomeOtherOperatingIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitment_2298e2d6-7b63-4bfe-a6ae-5a3b52ae882b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total loan commitments</link:label>
    <link:label id="lab_us-gaap_OtherCommitment_label_en-US" xlink:label="lab_us-gaap_OtherCommitment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitment" xlink:to="lab_us-gaap_OtherCommitment" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_IcfrAuditorAttestationFlag_1b251875-559e-4ccd-b3c2-9842bdd8cfbc_terseLabel_en-US" xlink:label="lab_dei_IcfrAuditorAttestationFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ICFR Auditor Attestation Flag</link:label>
    <link:label id="lab_dei_IcfrAuditorAttestationFlag_label_en-US" xlink:label="lab_dei_IcfrAuditorAttestationFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ICFR Auditor Attestation Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_IcfrAuditorAttestationFlag" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_IcfrAuditorAttestationFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_IcfrAuditorAttestationFlag" xlink:to="lab_dei_IcfrAuditorAttestationFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditLossAbstract_label_en-US" xlink:label="lab_us-gaap_CreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditLossAbstract" xlink:to="lab_us-gaap_CreditLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_NonVotingCommonEquivalentStockSeriesDMember_44587efa-cfae-417a-8db7-74c7a9ad09a1_terseLabel_en-US" xlink:label="lab_fbc_NonVotingCommonEquivalentStockSeriesDMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Voting Common Equivalent Series D</link:label>
    <link:label id="lab_fbc_NonVotingCommonEquivalentStockSeriesDMember_label_en-US" xlink:label="lab_fbc_NonVotingCommonEquivalentStockSeriesDMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Voting Common Equivalent Stock Series D [Member]</link:label>
    <link:label id="lab_fbc_NonVotingCommonEquivalentStockSeriesDMember_documentation_en-US" xlink:label="lab_fbc_NonVotingCommonEquivalentStockSeriesDMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Voting Common Equivalent Stock Series D</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NonVotingCommonEquivalentStockSeriesDMember" xlink:href="fbc-20251231.xsd#fbc_NonVotingCommonEquivalentStockSeriesDMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_NonVotingCommonEquivalentStockSeriesDMember" xlink:to="lab_fbc_NonVotingCommonEquivalentStockSeriesDMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_46d4b1a8-96e5-4d7b-9d4c-a00aba1cc880_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation expense related to restricted stock awards</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_OneToFourFamilyIncludingInterestRateLocksMember_001b9f2c-ac37-4ede-a238-0087cf495a39_terseLabel_en-US" xlink:label="lab_fbc_OneToFourFamilyIncludingInterestRateLocksMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">One-to-four family including interest rate locks</link:label>
    <link:label id="lab_fbc_OneToFourFamilyIncludingInterestRateLocksMember_label_en-US" xlink:label="lab_fbc_OneToFourFamilyIncludingInterestRateLocksMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">One-To-Four Family Including Interest Rate Locks [Member]</link:label>
    <link:label id="lab_fbc_OneToFourFamilyIncludingInterestRateLocksMember_documentation_en-US" xlink:label="lab_fbc_OneToFourFamilyIncludingInterestRateLocksMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">One-To-Four Family Including Interest Rate Locks</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_OneToFourFamilyIncludingInterestRateLocksMember" xlink:href="fbc-20251231.xsd#fbc_OneToFourFamilyIncludingInterestRateLocksMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_OneToFourFamilyIncludingInterestRateLocksMember" xlink:to="lab_fbc_OneToFourFamilyIncludingInterestRateLocksMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_PreferredStockDividendPaymentRateVariableRate_fb328738-80b8-4c2a-8588-4425b5a88575_terseLabel_en-US" xlink:label="lab_fbc_PreferredStockDividendPaymentRateVariableRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend payment variable rate</link:label>
    <link:label id="lab_fbc_PreferredStockDividendPaymentRateVariableRate_label_en-US" xlink:label="lab_fbc_PreferredStockDividendPaymentRateVariableRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Payment Rate, Variable Rate</link:label>
    <link:label id="lab_fbc_PreferredStockDividendPaymentRateVariableRate_documentation_en-US" xlink:label="lab_fbc_PreferredStockDividendPaymentRateVariableRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Payment Rate, Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_PreferredStockDividendPaymentRateVariableRate" xlink:href="fbc-20251231.xsd#fbc_PreferredStockDividendPaymentRateVariableRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_PreferredStockDividendPaymentRateVariableRate" xlink:to="lab_fbc_PreferredStockDividendPaymentRateVariableRate" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets_c1bf5ca7-6303-452c-8118-c9a88d7b6f1a_totalLabel_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets acquired</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets_label_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Assets</link:label>
    <link:label id="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets_documentation_en-US" xlink:label="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets" xlink:href="fbc-20251231.xsd#fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets" xlink:to="lab_fbc_BusinessCombinationProvisionalInformationInitialAccountingIncompleteAdjustmentAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorFirmId_0dfc4399-447b-49fa-a1a6-ce5231f13d7e_terseLabel_en-US" xlink:label="lab_dei_AuditorFirmId" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Firm ID</link:label>
    <link:label id="lab_dei_AuditorFirmId_label_en-US" xlink:label="lab_dei_AuditorFirmId" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Firm ID</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorFirmId" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorFirmId"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorFirmId" xlink:to="lab_dei_AuditorFirmId" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal_8d661474-dee7-416a-ab3f-d58981d316c2_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total state net operating loss carryforwards</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, State and Local</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_18392f63-0571-412f-a3c2-97b44294b261_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationAxis" xlink:to="lab_us-gaap_IncomeStatementLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_54da80c6-f9f7-4b3a-8141-707e61528e56_verboseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Investment Securities</link:label>
    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments in Debt and Marketable Equity Securities (and Certain Trading Assets) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanBenefitObligation_f64c6fe2-eb14-4401-ab2d-3fd94f5a423f_periodStartLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanBenefitObligation" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Projected benefit obligation at beginning of year</link:label>
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    <link:label id="lab_fbc_MoneyMarketCashEquivalentsMember_documentation_en-US" xlink:label="lab_fbc_MoneyMarketCashEquivalentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Money Market/Cash Equivalents</link:label>
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    <link:label id="lab_us-gaap_SubordinatedDebt_d2dadb48-8d87-42f9-9e9c-8c95f0201871_terseLabel_en-US" xlink:label="lab_us-gaap_SubordinatedDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated notes</link:label>
    <link:label id="lab_us-gaap_SubordinatedDebt_label_en-US" xlink:label="lab_us-gaap_SubordinatedDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subordinated Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubordinatedDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubordinatedDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubordinatedDebt" xlink:to="lab_us-gaap_SubordinatedDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_799e69c8-1c61-4e46-aaca-bd0b5a878a84_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear_965d8546-e306-4854-b8a0-b9290c7df001_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originated year two</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Two, Originated, Fiscal Year before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_4ca59ea1-b154-47ad-b85a-8217be1e4a3d_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities assumed</link:label>
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    <link:label id="lab_us-gaap_SubordinatedDebtMember_061d3fd5-8c46-47eb-b564-1ca7dca92b29_terseLabel_en-US" xlink:label="lab_us-gaap_SubordinatedDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated notes</link:label>
    <link:label id="lab_us-gaap_SubordinatedDebtMember_label_en-US" xlink:label="lab_us-gaap_SubordinatedDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subordinated Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubordinatedDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubordinatedDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubordinatedDebtMember" xlink:to="lab_us-gaap_SubordinatedDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_46c8582d-27d7-48c5-92b8-7622c80d9ac7_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesPeriodPastDueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllExecutiveCategoriesMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfBenefitObligationsInExcessOfFairValueOfPlanAssetsTableTextBlock_f19ee5c3-93e4-471f-bdd8-93e0c744dd9b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBenefitObligationsInExcessOfFairValueOfPlanAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Defined Benefit Plan, Plan with Projected Benefit Obligation in Excess of Plan Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBenefitObligationsInExcessOfFairValueOfPlanAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBenefitObligationsInExcessOfFairValueOfPlanAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Plan with Projected Benefit Obligation in Excess of Plan Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBenefitObligationsInExcessOfFairValueOfPlanAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBenefitObligationsInExcessOfFairValueOfPlanAssetsTableTextBlock"/>
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    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_c46a30b1-61ea-4923-94aa-3531cc0a1f09_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock"/>
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    <link:label id="lab_us-gaap_CommonStockValue_c39de0c1-8aee-4b48-b63d-0bfcd58a3b6e_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock at par 0.01 (916,666,666 and 666,666,666 shares authorized; 422,931,277 and 422,416,178 shares issued; and 415,982,036 and 414,934,628 shares outstanding, respectively)</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_5eb95b99-caaa-4c10-a584-655bc46060c6_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue"/>
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    <link:label id="lab_fbc_VariableInterestEntityNumberofEntities_f816be1b-9db7-492a-80af-7881be4fe81c_terseLabel_en-US" xlink:label="lab_fbc_VariableInterestEntityNumberofEntities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of variable interest entities</link:label>
    <link:label id="lab_fbc_VariableInterestEntityNumberofEntities_label_en-US" xlink:label="lab_fbc_VariableInterestEntityNumberofEntities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Number of Entities</link:label>
    <link:label id="lab_fbc_VariableInterestEntityNumberofEntities_documentation_en-US" xlink:label="lab_fbc_VariableInterestEntityNumberofEntities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Number of Entities</link:label>
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    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases_0fde5997-dfa4-4bcb-aefb-7d5cde27c803_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans and leases</link:label>
    <link:label id="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases_label_en-US" xlink:label="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Fee Income, Loans and Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndFeeIncomeLoansAndLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:to="lab_us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_9be9c232-1c68-44fe-b1fd-9629a3e39ef7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
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    <link:label id="lab_fbc_MultiFamilyLoanMember_c9756d16-5e4a-4696-8d93-7c780371e454_terseLabel_en-US" xlink:label="lab_fbc_MultiFamilyLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-family</link:label>
    <link:label id="lab_fbc_MultiFamilyLoanMember_label_en-US" xlink:label="lab_fbc_MultiFamilyLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Multi-Family Loan [Member]</link:label>
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    <link:label id="lab_us-gaap_CommitmentsAndContingencies_0738105f-9ea2-4ec7-8f57-9307b758b85f_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitment and contingencies (refer to Note 20)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingencies"/>
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    <link:label id="lab_us-gaap_PreferredStockLiquidationPreferenceValue_76ee8914-05c3-40a4-93e8-712460371dbf_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockLiquidationPreferenceValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Liquidation Preference, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockLiquidationPreferenceValue"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff_d065b3e5-47ef-46ea-a7d1-1800d17b17fa_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Originated year one</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year One, Originated, Current Fiscal Year, Writeoff</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_546433a2-48d0-452e-a1db-0af85de0a037_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gross realized losses</link:label>
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    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
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    <link:label id="lab_fbc_CommercialAndIndustrialLoanAndLeaseFinancingMember_6b3fede0-c99e-4310-ae17-cf8978df48fb_terseLabel_en-US" xlink:label="lab_fbc_CommercialAndIndustrialLoanAndLeaseFinancingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial and industrial loans and lease financing</link:label>
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    <link:label id="lab_fbc_FinancialAsset30To89DaysPastDueMember_9f44a31c-23db-455e-8a8d-85c6d4d8bad5_terseLabel_en-US" xlink:label="lab_fbc_FinancialAsset30To89DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans 30-89 Days Past Due</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanEquitySecuritiesMember_c3b1ab03-3f13-4da6-b229-aa3b83fdf325_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanEquitySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_115b67e1-d02a-4287-80a2-aedf8095568f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Financial Instruments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_3e6c812d-b604-4e09-8c61-0b2334f59bdf_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
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    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_c52e70bf-83c2-4c8f-ba80-dc33d5257231_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability [Abstract]</link:label>
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    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostChangeDueToSubsequentInterimMeasurementWeightedAverageExpectedLongTermRateOfReturnOnPlanAssets_367b7124-3b6e-42c7-bab0-9c4df29c082a_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostChangeDueToSubsequentInterimMeasurementWeightedAverageExpectedLongTermRateOfReturnOnPlanAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term inflation rate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostChangeDueToSubsequentInterimMeasurementWeightedAverageExpectedLongTermRateOfReturnOnPlanAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingNetPeriodicBenefitCostChangeDueToSubsequentInterimMeasurementWeightedAverageExpectedLongTermRateOfReturnOnPlanAssets"/>
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    <link:label id="lab_srt_ScenarioForecastMember_4824f49e-882b-4950-834a-79b2bbf6740d_terseLabel_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forecast</link:label>
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    <link:label id="lab_us-gaap_FairValueOptionLoansHeldAsAssetsAggregateDifference_4decc0bf-0c60-400a-9f22-2d1642b1e793_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionLoansHeldAsAssetsAggregateDifference" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Over / (Under) UPB</link:label>
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    <link:label id="lab_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic_52d5d51a-168e-42cf-a37c-d6164c4e31ff_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Income allocated to participating securities</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_5bc102fd-5a52-4d01-8b3b-e4aa37e60871_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_0f69c58c-acc7-48ab-b6cd-b1b0bfe4176f_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for (recovery of) credit losses on loans and leases</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal"/>
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    <link:label id="lab_us-gaap_TemporaryEquityLiquidationPreference_91dd2362-d684-4f14-a5d7-1fa36869e954_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncumulative convertible preferred stock</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityLiquidationPreference_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Liquidation Preference</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityLiquidationPreference" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityLiquidationPreference"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityLiquidationPreference" xlink:to="lab_us-gaap_TemporaryEquityLiquidationPreference" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_LoansHeldForSaleMember_1ddec1c7-45be-4534-b9ec-ae9e26ca0879_terseLabel_en-US" xlink:label="lab_fbc_LoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held for sale</link:label>
    <link:label id="lab_fbc_LoansHeldForSaleMember_label_en-US" xlink:label="lab_fbc_LoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Held-For-Sale [Member]</link:label>
    <link:label id="lab_fbc_LoansHeldForSaleMember_documentation_en-US" xlink:label="lab_fbc_LoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans that are intended to be sold into the secondary market on a whole loan basis or by securitizing the loans into securities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_LoansHeldForSaleMember" xlink:href="fbc-20251231.xsd#fbc_LoansHeldForSaleMember"/>
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    <link:label id="lab_us-gaap_EarningsPerShareAbstract_981faf86-f947-4fd6-8982-14c8f2f37e6a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareAbstract"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_65f40cfa-9d97-4b3e-974f-865653f9c388_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_TemporaryEquityConversionOfConvertibleSecurities_376e5c41-e29a-49a5-9a73-bff87bb91950_negatedTerseLabel_en-US" xlink:label="lab_fbc_TemporaryEquityConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common shares for the conversion of Series B/ C preferred, net</link:label>
    <link:label id="lab_fbc_TemporaryEquityConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_fbc_TemporaryEquityConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Conversion Of Convertible Securities</link:label>
    <link:label id="lab_fbc_TemporaryEquityConversionOfConvertibleSecurities_documentation_en-US" xlink:label="lab_fbc_TemporaryEquityConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Conversion Of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_TemporaryEquityConversionOfConvertibleSecurities" xlink:href="fbc-20251231.xsd#fbc_TemporaryEquityConversionOfConvertibleSecurities"/>
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    <link:label id="lab_fbc_DefinedBenefitPlanEquityLargeCapGrowthMember_4dcb51e1-a216-48a1-b3ce-cbb473e431f8_terseLabel_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquityLargeCapGrowthMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Large-cap growth</link:label>
    <link:label id="lab_fbc_DefinedBenefitPlanEquityLargeCapGrowthMember_label_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquityLargeCapGrowthMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Equity, Large Cap Growth [Member]</link:label>
    <link:label id="lab_fbc_DefinedBenefitPlanEquityLargeCapGrowthMember_documentation_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquityLargeCapGrowthMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Equity, Large Cap Growth</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_DefinedBenefitPlanEquityLargeCapGrowthMember" xlink:href="fbc-20251231.xsd#fbc_DefinedBenefitPlanEquityLargeCapGrowthMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_DefinedBenefitPlanEquityLargeCapGrowthMember" xlink:to="lab_fbc_DefinedBenefitPlanEquityLargeCapGrowthMember" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivableDeferredOriginationCosts_21c4d4f0-e6bc-420f-8460-7cc3ac6a89f2_terseLabel_en-US" xlink:label="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivableDeferredOriginationCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plus: deferred origination costs</link:label>
    <link:label id="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivableDeferredOriginationCosts_label_en-US" xlink:label="lab_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivableDeferredOriginationCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type And Direct Financing Leases, Lease Receivable, Deferred Origination Costs</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivableDeferredOriginationCosts" xlink:href="fbc-20251231.xsd#fbc_SalesTypeAndDirectFinancingLeasesLeaseReceivableDeferredOriginationCosts"/>
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    <link:label id="lab_fbc_NoninterestIncomeOtherOperatingIncomeLoss_d36ca8e4-f1b2-4098-913b-76955454f361_verboseLabel_en-US" xlink:label="lab_fbc_NoninterestIncomeOtherOperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_fbc_NoninterestIncomeOtherOperatingIncomeLoss_label_en-US" xlink:label="lab_fbc_NoninterestIncomeOtherOperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income, Other Operating Income (Loss)</link:label>
    <link:label id="lab_fbc_NoninterestIncomeOtherOperatingIncomeLoss_documentation_en-US" xlink:label="lab_fbc_NoninterestIncomeOtherOperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noninterest Income, Other Operating Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_NoninterestIncomeOtherOperatingIncomeLoss" xlink:href="fbc-20251231.xsd#fbc_NoninterestIncomeOtherOperatingIncomeLoss"/>
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    <link:label id="lab_us-gaap_InterestIncomeAndInterestExpenseDisclosureTableTextBlock_019c248a-ffad-7e58-9124-95ce313d079c_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeAndInterestExpenseDisclosureTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Total Interest Expense</link:label>
    <link:label id="lab_us-gaap_InterestIncomeAndInterestExpenseDisclosureTableTextBlock_label_en-US" xlink:label="lab_us-gaap_InterestIncomeAndInterestExpenseDisclosureTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income and Interest Expense Disclosure [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeAndInterestExpenseDisclosureTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeAndInterestExpenseDisclosureTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeAndInterestExpenseDisclosureTableTextBlock" xlink:to="lab_us-gaap_InterestIncomeAndInterestExpenseDisclosureTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff_70d585fb-10b4-47a0-9fa6-03987cae020c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Originated year three</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Three, Originated, Two Years before Current Fiscal Year, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansNetUnamortizedGainLossArisingDuringPeriodBeforeTax_c7538668-8eef-4563-8ad7-bf08367d944c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansNetUnamortizedGainLossArisingDuringPeriodBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net actuarial (gain) loss arising during the year</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansNetUnamortizedGainLossArisingDuringPeriodBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansNetUnamortizedGainLossArisingDuringPeriodBeforeTax"/>
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    <link:label id="lab_fbc_DebtSecuritiesAvailableForSaleExcludingInterestAndEquitySecuritiesCurrent_16b88381-ba89-4a02-85ba-4cbaf1ef4dd9_terseLabel_en-US" xlink:label="lab_fbc_DebtSecuritiesAvailableForSaleExcludingInterestAndEquitySecuritiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_fbc_DebtSecuritiesAvailableForSaleExcludingInterestAndEquitySecuritiesCurrent_label_en-US" xlink:label="lab_fbc_DebtSecuritiesAvailableForSaleExcludingInterestAndEquitySecuritiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available For Sale, Excluding Interest And Equity Securities, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_DebtSecuritiesAvailableForSaleExcludingInterestAndEquitySecuritiesCurrent" xlink:to="lab_fbc_DebtSecuritiesAvailableForSaleExcludingInterestAndEquitySecuritiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_bc59cf88-ad45-451c-9ee0-5618e5fc20d4_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock, acquired, shares (in shares)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockSharesAcquired" xlink:to="lab_us-gaap_TreasuryStockSharesAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_fbc_TemporaryEquityAndEquityParValueAbstract_97140120-23ef-4454-959b-aaae77b1d5e5_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityParValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Par Value</link:label>
    <link:label id="lab_fbc_TemporaryEquityAndEquityParValueAbstract_label_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityParValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity And Equity, Par Value [Abstract]</link:label>
    <link:label id="lab_fbc_TemporaryEquityAndEquityParValueAbstract_documentation_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquityParValueAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity And Equity, Par Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_TemporaryEquityAndEquityParValueAbstract" xlink:href="fbc-20251231.xsd#fbc_TemporaryEquityAndEquityParValueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_fbc_TemporaryEquityAndEquityParValueAbstract" xlink:to="lab_fbc_TemporaryEquityAndEquityParValueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_fe8e12bc-33d3-423f-9b4b-0e5049f8128e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
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    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems_895b0a5c-941b-4483-8185-edec0da94a28_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems"/>
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    <link:label id="lab_us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock_e3b4708f-e8ce-41a9-809f-4128a7d59dbd_terseLabel_en-US" xlink:label="lab_us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Nonvested Restricted Stock Shares Activity</link:label>
    <link:label id="lab_us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonvested Restricted Stock Shares Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock"/>
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    <link:label id="lab_fbc_FairValueOptionLoansHeldAsAssets_2eb0de7a-e9e7-43ac-b167-9d2b4ac7a24c_verboseLabel_en-US" xlink:label="lab_fbc_FairValueOptionLoansHeldAsAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_fbc_FairValueOptionLoansHeldAsAssets_label_en-US" xlink:label="lab_fbc_FairValueOptionLoansHeldAsAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Loans Held As Assets</link:label>
    <link:label id="lab_fbc_FairValueOptionLoansHeldAsAssets_documentation_en-US" xlink:label="lab_fbc_FairValueOptionLoansHeldAsAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Loans Held As Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_fbc_FairValueOptionLoansHeldAsAssets" xlink:href="fbc-20251231.xsd#fbc_FairValueOptionLoansHeldAsAssets"/>
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    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets_8b19a574-50df-491a-84ea-1dae1b864d97_terseLabel_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing fees, ancillary income and late fees</link:label>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets_label_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractually Specified Servicing Fee, Late Fee, and Ancillary Fee Earned in Exchange for Servicing Financial Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets"/>
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    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
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    <link:label id="lab_fbc_DefinedBenefitPlanEquityNonUSValueMember_4d2da3cc-e386-41bf-a6ee-38d70ee10a33_terseLabel_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquityNonUSValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">International value</link:label>
    <link:label id="lab_fbc_DefinedBenefitPlanEquityNonUSValueMember_label_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquityNonUSValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Equity, Non-US, Value [Member]</link:label>
    <link:label id="lab_fbc_DefinedBenefitPlanEquityNonUSValueMember_documentation_en-US" xlink:label="lab_fbc_DefinedBenefitPlanEquityNonUSValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Equity, Non-US, Value</link:label>
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    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_903bbf14-3f05-4f65-b31d-cfc35082c160_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:to="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMember_f4bb1e1f-f214-4f95-aa64-71ccd076f4b6_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FHLB advances</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMember_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank Advances [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FederalHomeLoanBankAdvancesMember"/>
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    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_87073101-e12f-436e-94ce-4d14c04693ee_verboseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mezzanine and Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_910d074e-0523-4389-b6e7-9513e25c2acc_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State and local &#8211; deferred</link:label>
    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred State and Local Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_LoanRestructuringModificationDomain_b599b2e4-e9dc-45fb-90cc-0dac00ae1ded_terseLabel_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Domain]</link:label>
    <link:label id="lab_us-gaap_LoanRestructuringModificationDomain_label_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoanRestructuringModificationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoanRestructuringModificationDomain"/>
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    <link:label id="lab_stpr_IN_019b92f5-4c09-72dc-9b67-725ed1e25f79_terseLabel_en-US" xlink:label="lab_stpr_IN" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indiana</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_543d48ef-f1a3-4eb2-8579-14fdcf11a42d_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total loans and leases held for investment, net</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_c2bc1675-a7f1-49f8-85ec-97a6c38a22a4_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total loans and leases held for investment, net</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_1081c715-f147-4227-ba7d-c788c7dd7660_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans held for investment</link:label>
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    <link:label id="lab_stpr_IL_019b92f4-20d6-72a2-bc0d-6e8aefa89339_terseLabel_en-US" xlink:label="lab_stpr_IL" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Illinois</link:label>
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    <link:label id="lab_us-gaap_NetIncomeLoss_8798ca0a-f2b0-4aa5-8383-4c4e1adb74fb_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_b7cb6eaa-063e-4c6c-bcbc-36871847edf5_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_a0c5b07c-c784-4f25-9ced-10bc65342116_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
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    <link:label id="lab_us-gaap_CapitalToRiskWeightedAssets_27064558-f54b-4ca9-b485-e22bda3c565c_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total capital, ratio</link:label>
    <link:label id="lab_us-gaap_CapitalToRiskWeightedAssets_label_en-US" xlink:label="lab_us-gaap_CapitalToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital Ratio, Actual</link:label>
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    <link:label id="lab_fbc_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_f5a73bea-f148-4571-b0be-1955de63eb67_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mezzanine preferred stock (in shares)</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_2669ec4d-ca94-495d-bd35-3bb5bc49e092_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Differences Between the Effective Tax Rate and the Statutory Federal Tax Rate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_55bd789d-8d16-4656-a85f-36125ca0ea13_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting period</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_a22866b6-d7e0-4ef6-b0ad-d3b7f6a45534_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other, net</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Other Adjustments, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments"/>
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    <link:label id="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember_049ce4d0-9e69-47e5-bfa1-6284b5bf35df_terseLabel_en-US" xlink:label="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net return on mortgage servicing rights</link:label>
    <link:label id="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember_label_en-US" xlink:label="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights (MSR) Impairment (Recovery) [Member]</link:label>
    <link:label id="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember_documentation_en-US" xlink:label="lab_fbc_MortgageServicingRightsMSRImpairmentRecoveryMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents the net return on mortgage servicing asset.</link:label>
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    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_c2c20608-8c46-4677-9522-465b2007602d_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
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    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesPrepaidExpenses_28b64fa6-82af-459f-877e-f72f052ee3db_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesPrepaidExpenses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Prepaid pension cost</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesPrepaidExpenses_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesPrepaidExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Prepaid Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesPrepaidExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesPrepaidExpenses"/>
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    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_75c8b1d1-4b59-4a48-afdd-ab23d9b55cae_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivablesPastDueTable"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_c794c3f4-0c40-4df7-be6f-8805b89f85ec_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term of contract</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Term of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseTermOfContract"/>
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    <link:label id="lab_fbc_SubordinatedNotesMaturingIn2030Member_f7bd1f9a-3c94-428a-976c-00acd2a54e2b_terseLabel_en-US" xlink:label="lab_fbc_SubordinatedNotesMaturingIn2030Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated notes maturing in 2030</link:label>
    <link:label id="lab_fbc_SubordinatedNotesMaturingIn2030Member_label_en-US" xlink:label="lab_fbc_SubordinatedNotesMaturingIn2030Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subordinated Notes Maturing In 2030 [Member]</link:label>
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    <link:label id="lab_stpr_FL_019b92f4-58bd-7db9-917d-c0bea96a9000_terseLabel_en-US" xlink:label="lab_stpr_FL" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Florida</link:label>
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    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_c348b61e-3d13-422c-b847-173921221419_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Offsetting Liabilities</link:label>
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    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_bf072981-c67b-470f-9e95-366a50dceae8_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
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    <link:label id="lab_us-gaap_DepositsMoneyMarketDeposits_6d11b108-5d73-4d26-a0ff-eb109278b17a_terseLabel_en-US" xlink:label="lab_us-gaap_DepositsMoneyMarketDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest-bearing checking and money market accounts</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfCompensationCostForShareBasedPaymentArrangementsAllocationOfShareBasedCompensationCostsByPlanTableTextBlock_9da959c1-ae41-4e17-b785-99540f7bf634_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCompensationCostForShareBasedPaymentArrangementsAllocationOfShareBasedCompensationCostsByPlanTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock Based Compensation Expense and Related Tax Benefit</link:label>
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    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
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    <link:label id="lab_us-gaap_StatementClassOfStockAxis_00ec18a1-6b9c-4cf2-865f-2fcda6955847_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember"/>
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    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_43732258-0061-45f5-a6b8-e79ec1a6a844_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Other</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesOther" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetirementPlanTypeAxis_5e58bf16-e030-4cf4-a659-b2ab50232555_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets_4dabd023-21fd-4454-9837-a196f124fc54_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Actual return on plan assets</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Plan Assets, Increase (Decrease) for Actual Return (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanActualReturnOnPlanAssets"/>
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    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_1a1f890f-07ce-48b0-a3f2-966642376851_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax benefit</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
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    <link:label id="lab_fbc_ProceedsFromSalePaymentsToAcquirePropertyPlantAndEquipment_baac6c78-c65f-4d7f-a703-f14745af9dd1_terseLabel_en-US" xlink:label="lab_fbc_ProceedsFromSalePaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchases of premises and equipment, net</link:label>
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    <link:label id="lab_fbc_SecuritizationOfLoansToMortgageBackedSecuritiesAvailableForSale_fa823d56-e477-4d09-ad96-b3cea7f9387d_terseLabel_en-US" xlink:label="lab_fbc_SecuritizationOfLoansToMortgageBackedSecuritiesAvailableForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Securitization of loans to mortgage-backed securities available-for-sale</link:label>
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    <link:label id="lab_fbc_FinancingReceivableWithGovernmentGuaranty_91e92a14-06c7-4b62-8104-a9fa9fabc98b_terseLabel_en-US" xlink:label="lab_fbc_FinancingReceivableWithGovernmentGuaranty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LGG loans</link:label>
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    <link:label id="lab_us-gaap_AllOtherCorporateBondsMember_019c24dc-5dc4-75da-9a0f-7df523549577_terseLabel_en-US" xlink:label="lab_us-gaap_AllOtherCorporateBondsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate and Other Bonds</link:label>
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    <link:label id="lab_fbc_TemporaryEquityAndEquitySharesIssuedAbstract_90648145-61b2-4633-a44c-f155020e6d34_terseLabel_en-US" xlink:label="lab_fbc_TemporaryEquityAndEquitySharesIssuedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares Issued</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
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    <link:label id="lab_stpr_MA_019b92f4-cf48-7be1-8d57-320ec0b990c0_terseLabel_en-US" xlink:label="lab_stpr_MA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Massachusetts</link:label>
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    <link:label id="lab_us-gaap_ContractualInterestRateReductionMember_8067d294-1de8-4b44-8cea-e0c1feea42fa_terseLabel_en-US" xlink:label="lab_us-gaap_ContractualInterestRateReductionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contractual Interest Rate Reduction</link:label>
    <link:label id="lab_us-gaap_ContractualInterestRateReductionMember_label_en-US" xlink:label="lab_us-gaap_ContractualInterestRateReductionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Interest Rate Reduction [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractualInterestRateReductionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractualInterestRateReductionMember"/>
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    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense_ba012329-b491-4ac4-a1e8-f54cb7757f6c_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax benefit</link:label>
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    <link:label id="lab_us-gaap_FairValueOfAssetsAcquired_e1989476-d5d0-473a-bb7b-b33e5d2ee9de_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOfAssetsAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of tangible assets acquired</link:label>
    <link:label id="lab_us-gaap_FairValueOfAssetsAcquired_label_en-US" xlink:label="lab_us-gaap_FairValueOfAssetsAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value of Assets Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOfAssetsAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOfAssetsAcquired"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss_8cfa3553-3924-4cee-a077-4829b304aa70_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest receivable</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss"/>
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    <link:label id="lab_us-gaap_ScheduleOfAllocationOfPlanAssetsTableTextBlock_390eca3c-c72a-4a40-814a-adc6fc523046_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAllocationOfPlanAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Allocation of Plan Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAllocationOfPlanAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAllocationOfPlanAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Allocation of Plan Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAllocationOfPlanAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAllocationOfPlanAssetsTableTextBlock"/>
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    <link:label id="lab_us-gaap_TransfersAndServicingAbstract_a1ac8f89-94fb-48b3-8b40-99d0148862e4_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers and Servicing [Abstract]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingAbstract_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transfers and Servicing [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingAbstract"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonValue"/>
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    <link:label id="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_SalesTypeAndDirectFinancingLeasesLeaseReceivablePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales-Type and Direct Financing Leases, Payment to be Received, Year One</link:label>
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    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
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    <link:label id="lab_us-gaap_InterestBearingDepositsInBanks_019be969-0af9-7ff8-b513-e4bd6c8b7e8a_terseLabel_en-US" xlink:label="lab_us-gaap_InterestBearingDepositsInBanks" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest-earning deposits and other securities with financial institutions</link:label>
    <link:label id="lab_us-gaap_InterestBearingDepositsInBanks_label_en-US" xlink:label="lab_us-gaap_InterestBearingDepositsInBanks" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest-Bearing Deposits in Banks and Other Financial Institutions</link:label>
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    <link:label id="lab_fbc_GainLossOnSalesOfMortgageServicingRights_8b5ee849-c4e1-4bc5-a2e8-c3cb962897e2_terseLabel_en-US" xlink:label="lab_fbc_GainLossOnSalesOfMortgageServicingRights" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gain on mortgage/servicing sale</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_b0260e9e-f1c1-48f3-a88b-b497e17db1e2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Allowance for credit losses on loans and leases</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_4dc91568-54b1-4bbc-b864-7587ac8b1a06_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Payment Arrangement, Option, Activity</link:label>
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    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued_6b7c5a36-2670-41d4-b2c4-0886b11c3487_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax accrued interest expense and penalties</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_81ab634f-653b-416a-b124-4ec266813817_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted average common shares outstanding (in shares)</link:label>
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    <link:label id="lab_stpr_NJ_019c24ac-4868-725f-b95d-36afe427b69b_terseLabel_en-US" xlink:label="lab_stpr_NJ" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New Jersey</link:label>
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    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate_552f1a34-5814-4349-b11c-45c40d9e32ec_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total amount of net unrecognized tax benefits that would have effective tax rate</link:label>
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    <link:label id="lab_us-gaap_WarrantsAndRightsOutstanding_94c6e136-ef7b-4267-a482-d70f15ca3a4c_terseLabel_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants proceeds amount</link:label>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstanding_label_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants and Rights Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantsAndRightsOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WarrantsAndRightsOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantsAndRightsOutstanding" xlink:to="lab_us-gaap_WarrantsAndRightsOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_8a6a7a19-4a17-449b-8d48-0db3303e2b07_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Computation of Basic and Diluted Net Loss Per Share of Common Stock</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Number</link:label>
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    <link:label id="lab_us-gaap_DepositLiabilitiesTypeTableTextBlock_11a9f59d-8e63-4656-8b6f-2f1b0a2c5274_terseLabel_en-US" xlink:label="lab_us-gaap_DepositLiabilitiesTypeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Deposit Liabilities, Type</link:label>
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    <link:label id="lab_us-gaap_SegmentReportingAbstract_39f19bca-28b9-44fe-b52b-6779738b4bf4_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
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    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedNumberOfShares_95f39bb4-c891-4628-94a3-824442fc6657_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedNumberOfShares" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Vested (in shares)</link:label>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_af0b9948-bb86-44b6-a049-3d7aac2d193d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanByPlanAssetCategoriesAxis_300b5a49-4269-4f41-affa-699a50493ccf_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanByPlanAssetCategoriesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Plan Assets, Category [Axis]</link:label>
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    <link:label id="lab_fbc_FinancingReceivableRecordedInvestment_cc8e803a-9841-44ba-85a6-3ec724b009ca_totalLabel_en-US" xlink:label="lab_fbc_FinancingReceivableRecordedInvestment" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total non-accrual loans</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_d6e5ae8a-19c6-435f-aa9a-358f0fe19e67_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross realized gains (losses)</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsFiveFiscalYearsThereafter_013b2fea-efc0-42bc-9fed-7f3d4a0a00b1_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsFiveFiscalYearsThereafter" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2031 and thereafter</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParentAbstract_0afcf576-4369-49ba-9687-64a00246f71d_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax impact reported in stockholders&#8217; equity related to:</link:label>
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