A termination rule based on a critical funding ratio is proposed for a pension guarantee fund (PGF) that considers closing an underfunded pension plan. This ratio is determined by solving an expected utility maximization problem on behalf of plan beneficiaries subject to two constraints designed to preserve the PGF's viability. The first is an upper bound on the PGF's annual intervention probability; the second, a restriction on the expected shortfall of an underfunded pension plan that is not closed. Both too low and too high critical funding ratios hurt beneficiaries’ interests, depending on their degree of risk aversion.