This paper develops an equilibrium search model with endogenous job destructions and where firms decide at the time of job entry how much to invest in match-specific human capital. We first show that job destruction and training investment decisions are strongly complementary. It is possible that there are no firings at equilibrium. Further, training investments are confronted to a hold-up problem making the decentralized equilibrium always inefficient. We show therefore that both training subsidies and firing taxes must be implemented to bring back efficiency.