We consider complex networks where line failures occur indirectly as line flows are influenced by fluctuating input at nodes, a prime example being a power grid where power is generated by renewable sources. We examine the propagation of such emergent failures in the small noise regime, combining concepts from statistical physics and the physics of power flow. In particular we characterize rigorously and explicitly the configuration of inputs responsible for failures and cascades, and analyze the propagation of failures, which often is not of nearest-neighbor type.