The exposure of banks to systemic risk in financial networks usually requires large bailouts of taxpayer money with long-lasting and damaging societal consequences. We examine whether the banking network can reduce systemic risk from within by selfishly cancelling the debts of banks in distress. This operation can in principle reduce losses and prevent default cascades. We define an abstract model to simulate the ensuing strategic game on randomly generated financial networks, where each systemically important bank independently decides how likely it is to cancel some debts of insolvent banks. We compute the equilibrium of the induced empirical game with the empirical game-theoretic analysis and analyse its efficiency by measuring the price of anarchy. Our results show that selfish debt cancellation can reduce systemic risk when adopting the equilibrium strategy profile. However, our results also indicate that the efficiency of the equilibrium can be low and relatively few banks cancel debts at equilibrium, and we explain the reason for this through analysis of the banks’ incentives and game dynamics.