SEOUL—Caught halfway into a multicountry escape from North Korea, 13 individuals detained in Vietnam reached safety last month due to an unexpected helping hand: the U.S. government.

A group of U.S. diplomats, including some involved in disarmament talks with the Kim Jong Un regime, intervened after videos surfaced showing two female detainees wrapped under blankets following failed suicide attempts, according to people familiar with the episode. Both women had feared being repatriated to the North where they likely would...