It is worth investigating the existence of cooperation, which is costly for the actor but beneficial to the recipient (precisely because it is costly for the former). If players, when they approach defectors, stop their relationship with them, cooperation can pay off and favorably emerge in the course of evolutionary dynamics. The present study examines the situation in which animals, even when they want to cooperate, sometimes lack the necessary resources, and are thereby prevented from cooperating with others. In addition, it is also considered that the underlying information about the presence or absence of these resources can be conveyed to the opponent player. Here, the opponent who defects-has no resources for cooperation-may be a cooperator or a defector. Therefore, it is not clear which behavior is more likely to evolve, if it is keeping the interaction with such an opponent (i.e., being trustful) or stopping the interaction with such an opponent (i.e., being not trustful). By using evolutionary game theory, it is revealed that those who want to keep the interaction with those without the resources to cooperate are favored by natural selection. This study sheds new light on the role of keeping and stopping interaction in the evolution of cooperation under variable availability of resources.