In usa.gov, the search: "no match letter" "internal audit" gets one hit, HEARING ON IMPACTS OF BORDER SECURITY AND IMMIGRATION ON WAYS AND MEANS PROGRAMS HEARING BEFORE THE COMMITTEE ON WAYS AND MEANS U.S. HOUSE OF REPRESENTATIVES ONE HUNDRED NINTH CONGRESS SECOND SESSION JULY 26, 2006. The search: "security numbers" "voluntary audits" gets 4 hits; "security numbers" "voluntary audit" gets 5.
Even in Google, the search "security numbers" "voluntary audit" gets only 22 hits, and it may be worthwhile to scan through them. But the search: "no match letters" "voluntary audits" gets 30 hits and seems to find more discussions of the issue of companies firing workers without valid SSNs.
Another Radical Reference librarian found several sites that discuss questions of companies’ rights and responsibilities. Zamora v. Elite Logistics Inc. was a discrimination ruling, but it shows a company suspending an employee on the company's own initiative (as opposed to an edict of the federal government). Another possible line is the National Immigration Law Center (NILC) Social Security Administration "No-Match" Letters page. This page links to a number of cases, including court injunctions, instructions to employers, and restraining orders in some specific cases. NILC has a summary of the no-match letter injunction issued by the US District Court of Northern California.
But this is definitely a legal question, and would require a competent immigration attorney to give a definitive answer. Some preliminary research on your own might include the free online US Code search . The search: employers and 'social security numbers' gets 9 sections. Once you get into these very long full text laws, you can use CTRL-F to navigate to specific words; such as audit, voluntary, termination, etc. For less legalistic discussion, you might try searching public library databases such as Masterfile Premier. The search: companies and hiring illegal gets 23 hits; employers and hiring and illegal gets 161; employers and hiring illegal gets 61, security numbers and illegal and firing gets 1, security numbers and "no match letters" gets 5, etc., just to give a few possible examples.
At the other extreme, at large academic libraries you might have on-site access to legal databases such as Lexis Academic, where for example, US and Canadian Law Reviews gets 19 hits for the search: security numbers and "no match letters". These would have many hundreds of citations to earlier cases, other reviews, and legal articles and texts.
