This paper presents a self-organizing protocol for dynamic (unstructured P2P) overlay networks, which allows to react to the variability of node arrivals and departures. Through local interactions, the protocol avoids that the departure of nodes causes a partitioning of the overlay. We show that it is sufficient to have knowledge about 1st and 2nd neighbours, plus a simple interaction P2P protocol, to make unstructured networks resilient to node faults. A simulation assessment over different kinds of overlay networks demonstrates the viability of the proposal