This article proposes a fully distributed energy management algorithm for dc microgrids, resilient to different faults. Specifically, we employ distributed model-predictive control to deal with the uncertainty that characterizes the microgrid operation. The optimization problem is solved at each time step through a distributed optimization algorithm, which has three main advantages: 1) agents of the network require a small computational power; 2) local information is not shared among the network nodes, hence preserving a certain level of privacy; and 3) it is suitable for implementation in large-scale systems. The resilience property of the algorithm stems from additional constraints that are enforced in order to store in the system enough energy to sustain the microgrid in the case of utility grid or line fault. Simulation results show that the algorithm is suitable to schedule the operation of agents that are always connected to the microgrid (e.g., loads) as well as agents that may be connected and disconnected (e.g., electric vehicles).