We characterize optimal unconventional monetary and fiscal-financial policies within a tractable New Keynesian model featuring a monetary policy cost channel. State-dependent deposit tax-subsidy interventions remove the zero lower bound constraint on the nominal interest rate, thereby minimizing output and price fluctuations following both supply-driven and demand-driven liquidity traps. Specifically, deposit subsidies circumvent the inflation-output trade-off arising from stagflationary shocks by enabling the implementation of negative nominal interest rates. Moreover, deposit taxes facilitate modest interest rate hikes to escape deflationary traps. Notably, discretionary and commitment policies with deposit taxes / subsidies deliver virtually equivalent welfare gains, rendering time-inconsistent forward guidance schedules unnecessary.