This paper considers the safety problem for a group of target objects receiving energy or resources from a network infrastructure under a negative influence on its components that violates the links between the objects and the sources of energy or resources. We describe the well-known solution approaches for the network stability problems. In addition, we analyze the specifics of the search problem for the failed network components that violate the functionality of the target objects, also suggesting some solution methods and approaches to optimize calculations. Finally, we give an example to illustrate the failure search algorithm.