On a sweltering day in August 2012, Ana Duran heard dogs barking in the distance. For two days, she and several other migrants had been wandering, thirsty and disoriented, through grassland and spindly mesquite trees in southern Arizona. Now they could see four federal agents running toward them.

Duran, a petite woman in her early thirties, with soft, rounded features and strawberry-blond hair, had fled Guatemala to escape her abusive husband, from whom she had separated two years earlier. Duran had recently sought a formal protective order against him, but he still came to her house, in an industrial…