A no-match letter from the Social Security Administration is not the same as an immigration audit, which would be conducted by Immigration and Customs Enforcement. And some of the Social Security discrepancies involve minor clerical issues, like a missing digit or a spelling mistake in an employee’s name.

“Social Security is not a law enforcement agency,” said Mark Hinkle, the agency’s acting press secretary. “Our role is limited in scope to trying to ensure we credit each employee with his or her earnings.”

But the letters effectively require business owners to check whether the employees identified are properly documented. And in a potential ICE audit, employers who fail to investigate a no-match letter — or to act on what they find — could be deemed to have “constructive knowledge” of an employee’s immigration status, exposing them to hefty fines and possible criminal charges.

The last time the federal government sent a large number of no-match letters was more than a decade ago, when President George W. Bush was in office. Amid a broader crackdown on illegal immigration, the Trump administration has revived the process, at the same time that ICE has upped the frequency of its audits. In fiscal 2018, the agency initiated nearly 6,000 I-9 audits, a more than 400 percent increase from the previous year. And the ICE raids in Mississippi this month, which swept up hundreds of undocumented employees at agricultural plants, underscored the specter of increased enforcement across the food industry.

The experiences of two restaurant owners in New York City show how the pressures that face the industry have elicited strikingly divergent responses. The owners spoke on condition of anonymity because they did not want to attract attention from ICE.

One of them, who owns a restaurant group with locations in New York and Miami, said he had consulted with five different law firms about how to respond to the no-match letters, which he said named 350 of his employees, or about a quarter of his staff. At the advice of several of those lawyers, he said, he is considering firing employees who cannot produce documentation. He has also hired a company to inspect the I-9 forms of all future employees.

Over the past few months, a number of his employees have left of their own accord, he said, concerned that the no-match letters could portend a federal immigration raid.