The first families arrived in 1896. They drained the swamp to reach the fertile earth below, built a canal system and divided up the land. Their celery cultivation gave rise to a community named Celeryville that still exists, though growers have moved on to other crops.

Their descendants — the Wierses, Buurmas and Holthouses — now grow more than three dozen kinds of vegetables sold through Kroger, Meijer, Walmart and other retailers.

For decades, the farmers have relied on migrant labor from spring to fall. Depending on how quickly they work, field workers can earn up to $18 an hour, compared with Ohio’s $8.15 minimum hourly wage. Many return year after year to do the strenuous seasonal work, sometimes in temperatures that soar to 100 degrees. (Local residents largely steer clear.)

Seven in 10 field workers nationwide are undocumented, according to estimates by the American Farm Bureau Federation. In Willard, it is probably no different.

“Without the Hispanic labor force, we wouldn’t be able to grow crops,” said Ben Wiers, a great-grandson of the pioneer Henry Wiers, who bought five acres here in 1896, noting that he considers many workers at Wiers Farms, which cultivates more than 1,000 acres of produce under the Dutch Maid label, to be friends.

But beefed-up border enforcement has slowed the flow of workers who enter the country illegally. Last year, a shortage forced Mr. Wiers and the other growers to leave millions of dollars’ worth of produce in the fields.

This year could be worse. The Trump administration has encouraged local law enforcement across the country to help identify deportable individuals for the federal authorities, making long-distance travel risky for those already in the country without legal status.