Some of these defections have been hard to miss. In December, more than 10 players from the Eritrean national soccer team absconded to Kenya during a tournament. In 2004, some Eritrean refugees being sent home from Libya were so desperate not to return that they hijacked the plane.

Many never make it out. One of Mr. Awet’s friends recently won a four-year, $200,000 scholarship to a prestigious American university. “He should have been sent out with a garland of flowers,” said the boy’s father, with tears in his eyes.

Instead, the boy was arrested trying to defect in time to register for classes. He was drafted into the military and deployed near Eritrea’s southern border, one of the hottest places on earth.

Image Many young Eritreans complain of being chained to government jobs in Asmara. Credit... Shawn Baldwin for The New York Times

Mr. Awet was lucky. Dressed in an extra, extra large gallebeyah (a long flowing gown common in the Muslim world), he sneaked through Sudan and then on to Kenya and Dubai. He is now camped out in the basement of an American family’s home here, doing push-ups, working on his jump shot, playing on a Wii set with the family’s children and trying to get into an American college or prep school.

A big reason why he has gotten this far is Matthew Smith, a gregarious, athletic American diplomat who befriended Mr. Awet a couple years ago on a basketball court in Asmara, Eritrea’s capital, where Mr. Smith was working. Mr. Smith was impressed by the young man’s game, but more than that, he was moved by Mr. Awet’s burning ambition to break out of his hermetically sealed world.

“He wanted more, and I could relate to that,” said Mr. Smith, whose father was a taxi driver in Brooklyn. “Who would’ve ever thought the kid of a cabbie and nanny could be a diplomat?”