NGA KHU YA, Myanmar—Most of Abdul Solay’s family joined last year’s vast exodus of Rohingya from Myanmar, as government troops torched homes and opened fire on villages in a spasm of ethnically motivated violence. Mr. Solay decided to stay behind—and now he is struggling to survive.

Jobless and landless, the 22-year-old ekes out a living catching fish in a nearby stream. His family’s five cows—once a source of wealth—were confiscated. If he ventures into town, he says, he is taunted by members of Myanmar’s Buddhist majority,...