LAREDO, Tex. — Two weeks ago, a police officer on a routine patrol here was approached by six men frantically waving for him to stop. The men, all undocumented immigrants, told a harrowing tale.

With the help of smugglers, the men had crossed the Rio Grande a few days earlier. After being shuttled from one house to the next, they ended up at a mobile home in central Laredo, a city of 250,000 mostly Latino residents along the Mexican border. Unable to pay the smugglers the amount demanded for their passage, the men were threatened and locked in the house without food or water. They kicked out a back window to escape.

Hours later, when a squad of United States Border Patrol agents and local police officers descended on the mobile home, one man was still there. He said he was waiting to be taken to his next destination since he had paid his first installment of smuggling fees — $2,500. He expected to pay an additional $3,500 down the road.