When Inge Gabel of North Tonawanda, N.Y., watched her son Matthew disappear through the airport gate for a year abroad before college, she felt desolate. Her daughter was long gone, and now Matthew was also leaving. But her nest wasn't quite empty. Michael, 17, a recently arrived exchange
student, put his arms around her and consoled her. "Mom," he said, "we're gonna get through this." It was a spur-of-the-moment comment from a Costa Rican whom she had known for just two weeks, but it turned out to be remarkably prescient.
Michael's yearlong stay with Inge, 56, a hair stylist, and her...