According to the safety account of knowledge, one knows that p only if one's belief could not easily have been false. An important issue for the account is whether we should only examine the belief in the target proposition when evaluating whether a belief is safe or not. In this paper, it is argued that if we only examine the belief in the target proposition, then the account fails to account for why beliefs in necessary truths could fall short of knowledge. But, if we also examine beliefs in other relevant propositions, then the account fails to preserve epistemic closure. Therefore, the safety account cannot find a safe path between epistemic closure and necessary truths.