We study how decentralized transfers, originated by a selfish motive to preserve direct links, affect the resilience of a network against a shock. Well-off agents transfer resources to other agents in order to prevent the shock from reaching their neighbors. We show that the connectivity of a well-defined portion of the network, specifically, the propagation network, determines the resilience of the entire network. We also show how, although transfers are allocated to a subset of agents, the resilience effect of these transfers is amplified. Lastly, we show that the wealth distribution impacts resilience by determining the incentives of the agents to transfers resources.