When Dayana Castro heard that the U.S. asylum appointment she waited over a year for was canceled in an instant, she had no doubt: She was heading north any way she could. The 25-year-old migrant, her husband and their 4- and 7-year-old children had nothing left at home in Venezuela.

President Donald Trump’s plans to seal the U.S.-Mexico border and conduct mass deportations might soon run into a major roadblock: Mexico and the countries where the immigrants come from might not accept some of them back.