HAMAMATSU, Japan  Rita Yamaoka, a mother of three who immigrated from Brazil, recently lost her factory job here. Now, Japan has made her an offer she might not be able to refuse.

The government will pay thousands of dollars to fly Mrs. Yamaoka; her husband, who is a Brazilian citizen of Japanese descent; and their family back to Brazil. But in exchange, Mrs. Yamaoka and her husband must agree never to seek to work in Japan again.

“I feel immense stress. I’ve been crying very often,” Mrs. Yamaoka, 38, said after a meeting where local officials detailed the offer in this industrial town in central Japan.

“I tell my husband that we should take the money and go back,” she said, her eyes teary. “We can’t afford to stay here much longer.”