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We study the effects of financial frictions on firm exit when firms face large liquidity shocks. We develop a simple model of firm cost-minimization, where firms’ borrowing capacity to smooth temporary shocks to liquidity is limited. In this framework, firm exit arises from the interaction between this financial friction and fluctuations in cash flow due to aggregate and sectoral changes in demand conditions, as well as more traditional shocks to productivity. To evaluate the implications of our model, we use firm level data on small and medium sized enterprises (SMEs) in 11 European countries. We confirm that our framework is consistent with official failure rates in 2017–2019, a period characterized by standard business cycle fluctuations. To capture a large liquidity shock, we apply our framework to the COVID-19 crisis. We find that, absent government support, SME failure rates would have increased by 6.01 percentage points, putting 3.1% of employment at risk. Our results also show that in the presence of financial frictions and in the absence of government support, the firms failing due to COVID have similar productivity and growth to firms that survive COVID.