A security’s liquidity properties have been studied in terms mean and variance—liquidity level and liquidity risk, respectively. This paper explores tail events—liquidity disaster risk. The idea is that liquidity might not be an issue for investors in normal market conditions. But, it becomes a first-order concern if the security is `trapped’ in an illiquid state, in particular if this state is persistent so that waiting a day will not restore liquidity. A Markov regime-switching model is used to identify liquidity traps empirically. These are defined as the security being stuck in an illiquid regime for at least a week. The model is estimated for an unbalanced sample of 2147 stocks from 1963 through 2008. Standard Fama-MacBeth regressions show that a one standard deviation increase in the probability of a liquidity trap increases annual returns by 1.1%. And, this premium has increased over time.