Gary Zabroski started working for General Electric Co. in 1976, at an aviation factory in his hometown of Lynn, Mass. The job paid well, came with benefits and, for Mr. Zabroski, provided a career ladder for a man with a high- school education who started out cleaning toilets.

“You had a job for life if you had gotten in there,” said Mr. Zabroski, 61 years old. He rose to punch-press operator and retired in 2016, after working 40 years at the century-old plant, which roared to life during World War II and still churns out...