When 20-year-old Carmelo Padilla decided to leave his pueblo in the Mexican state of Jalisco for the United States, he had a few coins in his hand and an unshakeable idea in his mind: “I had nothing,” he would later tell his five children, “so there was nothing to lose.”

By the time he died two weeks ago, at age 75, Mr. Padilla, who spent years working at the Nunes dairy in the Point Reyes…