In a theoretical model of the Diamond-Dybvig style, in which deposit-taking banks and financial markets coexist, bank behavior is analyzed taking into account a positive ex-ante probability of a future financial crisis. We focus on the role of the interaction of market liquidity and banks' funding liquidity in the propagation of shocks in the financial system. Our findings suggest that in particular bank-dominated financial systems are prone to contagious bank runs due to asset price deteriorations as a consequence of fire sales of assets in financial markets. Nevertheless, banks only prefer holding liquidity buffers to weather future crises if the ex-ante crisis probability exceeds a certain threshold. Moreover, central bank interventions are shown to have destabilizing effects because they reduce banks' incentives to hold liquidity buffers. This can be interpreted as a justification for prudential regulation in terms of minimum liquidity buffer requirements.