Agents may form coalitions. Each coalition shares its endowment among its agents by applying a sharing rule. The sharing rule induces a coalition formation problem by assuming that agents rank coalitions according to the allocation they obtain in the corresponding sharing problem. We characterize the sharing rules that induce a class of stable coalition formation problems as those that satisfy a natural axiom that formalizes the principle of solidarity. Thus, solidarity becomes a sufficient condition to achieve stability. •We study coalition formation problems induced by sharing rules.•We characterize the rules that induce a class of stable coalition formation problems.•We focus on a natural axiom formalizing the principle of solidarity.•Solidarity becomes a sufficient condition to guarantee stability.