Japan’s conundrum: It needs foreign workers. It doesn’t want immigrants.

When it comes to foreign workers, Japan has a reputation to overcome.

Shi Jianhua has firsthand experience. In 2015, she migrated from China to Japan in search of life-transforming wages. “The agency told me going abroad for three years would change the economic situation of my family,” Ms. Shi says.

Back home in mountainous Hubei province, her husband worked in construction, and after the couple added a second child, expenses had begun to pile up. Ms. Shi’s plans to migrate had been methodical. She’d shelled out RMB 50,000 ($7,300) for Japanese language training, plus another RMB 38,000 ($5,500) in fees to a placement agency to enter Japan’s technical intern training program, created by the Japanese government to provide training and skills to workers from developing economies.

Once Ms. Shi landed at a quality control

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