The fatal flaw in the Border Patrol’s rescue program: The Missing Migrant Program is meant to prevent deaths, but instead it may be causing them.

For over a decade, local authorities in U.S. border towns have redirected calls from lost Spanish-speaking callers to the Border Patrol, the subagency of the U.S. Customs and Border Protection (CBP) that pursues and arrests border crossers. The agency’s Missing Migrant Program is the federal government’s primary response to...