The debt capacity of an asset is the maximum amount that can be borrowed using the asset as collateral. We model a sudden collapse in the debt capacity of good collateral. We assume short‐term debt that must be frequently rolled over, a small transaction cost of selling collateral in the event of default, and a small probability of meeting a buy‐to‐hold investor. We then show that a small change in the asset's fundamental value can be associated with a catastrophic drop in the debt capacity, the kind of market freeze observed during the crisis of 2007 to 2008.