This paper considers a novel theoretical argument allowing for the presence of duration dependence in individual exit rates of unemployment. If unemployed are ex ante heterogenous and if their skills are imperfectly observable, firing of the least able is an endogenous phenomenon that unemployed have an incentive to hide. Then, the unemployment duration conveys a (negative) signal about the quality of the worker, which firms use to evaluate his employability. A decrease in firing costs can make the economy topple from an equilibrium with unemployment, but without state dependence, over an equilibrium with discrimination against the long-term unemployed.