He noted, “The most obvious way that they would have become green card holders is by being the parents of a U.S. citizen—i.e., Melania Trump.”

Mr. Yale-Loehr, who has represented military deserters seeking asylum in the United States and co-directs the asylum clinic at Cornell Law School, said that in the past those who have fled the military from governments of U.S. adversaries have been more likely to gain asylum. “If you’re fleeing a government that the United States supports, like Canada, you’re more likely to lose asylum,” he noted. “But if you’re fleeing a government like Venezuela that the United States opposes then you’re more likely to win asylum, even if the facts are similar.”