DEL RIO, Texas—American taxpayers are increasingly funding the passage of a constant flow of migrants who ultimately cross illegally into the United States, according to new reports. A United Nations “cash-based interventions” program provides migrants heading to the U.S. border with debit cards, help with housing, transport, and medical assistance. The assistance is accessible in cities on the well-traveled routes from Latin America through Mexico. Thousands of migrants converge in southern Mexico where they apply for asylum—which gives them unfettered travel in Mexico—then most head directly to the U.S. border, where they cross illegally and claim asylum again. Migrants there are issued debit cards that reload each month, according to Todd Bensman, who is reporting from the city of Tapachula at Mexico’s southern border with Guatemala. Bensman is the senior national security fellow at the Center for Immigration Studies. In Tapachula on Jan. 14, a Haitian man was waiting for …