After more than two years of enduring Islamic State’s harsh rule, desperation trumped fear for Assad Ali Hassan and other residents of Faziliya, Iraq.

A few dozen militants controlled the village near the ISIS stronghold of Mosul with torture, fear and bureaucracy, recounted some who survived the occupation. The small band were the only ones with weapons, enabling them to exert outsize power over the 7,000 villagers, said Muhammad Ayub, an English-speaking graduate of Mosul University.

“Sometimes...