With increasing threats by large attacks or disasters, the time has come to reconstruct network infrastructures such as communication or transportation systems rather than to recover them as before in case of accidents, because many real networks are extremely vulnerable. Thus, we consider self-healing mechanisms by rewirings (reuse or addition of links) to be sustainable and resilient networks even against malicious attacks. In distributed local process for healing, the key strategies are the extension of candidates of linked nodes and enhancing loops by applying a message-passing algorithm inspired from statistical physics. Simulation results show that our proposed combination of ring formation and enhancing loops is particularly effective in comparison with the conventional methods, when more than half damaged links alive or are compensated from reserved ones.