WILLIAMSBURG, Va. — IN 1965, the secretary of labor, Willard Wirtz, stood under a porch light in Belle Glade, Fla., facing a crowd of guest workers from the Caribbean. Mr. Wirtz could smell sweat and burned sugar cane on their clothes but couldn’t see them, which was how the workers wanted it. Guest workers were often deported and blacklisted for striking or simply questioning whether they had been paid what they were owed.

“I would hear their voices — they would ask questions,” Mr. Wirtz recalled, but “they weren’t going to be identified.”

Congress had just terminated the famously exploitative Bracero Program for Mexican guest workers in response to reports of miserable pay and working conditions and farm employers’ illegal use of braceros as strikebreakers. The last of these workers — 4.5 million over the program’s lifetime — were just leaving when Mr. Wirtz visited Belle Glade to investigate the federal government’s remaining guest-worker program, known as H-2, which annually imported roughly 15,000 men from the Caribbean....