We endogenize separation in a search model of the labor market and allow for bargaining over the continuation of employment relationships following productivity shocks to take place under asymmetric information. In such a setting separation may occur even if continuation of the employment relationship is privately efficient for workers and firms. We show that reductions in the cost of separation, owing for example to a reduction in firing taxes, lead to an increase in job instability and, when separation costs are initially high, may be welfare decreasing for workers and firms. We furthermore show that, in response to an exogenous reduction in firing taxes, workers and firms may switch from rigid to flexible employment contracts, which further amplifies the increase in job instability caused by policy reform.