She said that she had been a committed citizen of the caliphate, but that hunger had forced her to surrender. For weeks, she said, she and her daughters subsisted on animal feed. Another woman spoke of scavenging for a plant that grows in the crevices between houses and in traffic circles, which she boiled and forced herself to eat.

The increasing peril that the Islamic State’s own families were subjected to was evident in the number of people who showed up every day with injuries.

One woman, her leg torn by shrapnel, was lifted from an arriving truck and held up as she hopped to the spot where other women were waiting to be screened. An older man collapsed on a mattress, suffering from a back injury. A woman in her 20s made it to the processing point, only to die soon after she arrived. Her family could do little beyond covering her with a blanket.

A schoolgirl from Turkey, the daughter of an Islamic State family, was sitting wrapped in a blanket, unable to stand because of her injuries from a mortar round. And a 6-year-old boy was rushed to a first aid station staffed by a group of recently arrived American aid workers.

“He’s not going to make it. His pulse is too low,” warned one of the paramedics, Jason Torlano of Yosemite, Calif., a member of an aid group called the Free Burma Rangers. The boy began trembling and whimpering in pain, straining from wounds to his head, arm and leg. The medics wrapped him in a heated blanket and tried to find a vein to start an IV drip, the bag of fluid taped to the hood of a Toyota Land Cruiser. “Hey, buddy,” the aid worker said, as the boy began to lose consciousness. “Stay with me.”

His mother stood nearby, repeatedly lifting the black fabric covering her face to wipe her eyes with a piece of Kleenex.

She said that she was from Aleppo and that her husband had been killed in an airstrike, but she denied being part of the Islamic State. Security forces from the Kurdish militia said that they considered her and the majority of the others who have arrived to be the wives and children of Islamic State members: Why else, they said, would a woman and a child who are not natives of the area make their way into an active war zone?