In this paper we consider a moral hazard problem, in which the agent after receiving his wage contract but before undertaking the costly effort can borrow on his future wage earnings. The game between the agent and potential lenders is modelled as an infinite stochastic game with an exogenous stopping probability. We show that the principal cannot design a wage scheme that is robust to hedging by the agent. In particular, we show that, if the exogenous stopping probability is non zero, the principal's wage offer will be followed by several rounds of borrowing by the agent. This is compared to the recontracting-proofness equilibria which most of the literature has concentrated on, assuming that this stopping probability is zero. Furthermore, we show that the equilibrium of the model with a strictly positive stopping probability does not converge to the equilibrium of the model in which it is zero. We also find that the principal's profit is lower, the maximum wage payment can be higher and effort is lower.