BROWNSVILLE, Tex. — After long hours at his day job, Sergio Cordova was driving home to pick up supplies and clothing for the tired and hungry asylum seekers who were camped out just a few miles away, in Matamoros, Mexico, waiting to be let in.

It was cold and raining and miserable. “Zero tolerance” at the United States border meant they were stuck outside.

From behind the wheel of his silver Honda Pilot, Mr. Cordova pointed to a squat, beige building called Casa Presidente.

“That’s where they house the kids,” he said as we cruised down Ruben M. Torres Sr. Boulevard.

He was referring to the babies and toddlers seized by border agents from the hundreds of migrant parents they arrested for illegal entry last spring under President Trump’s “family separation” policy. Miles down the road, he gestured toward a converted Walmart housing the older children, Casa Padre.