More likely just a complete ban from re-entering the USA again. Isn't it primarily a U.S. Citizenship & Immigration Services (USCIS) rather than FBI issue?
Per
https://www.huffpost.com/entry/immig...b0ed1f464c0e3a etc
Quote:
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A consular officer at a U.S. Embassy or Consulate abroad can deny a nonimmigrant visa application where a foreign national failed to maintain his or her nonimmigrant status by, for example, engaging in unauthorized employment or for misrepresentation on the nonimmigrant visa application by failing to disclose violations of previous nonimmigrant status.[10] (5) Ineligibility for adjustment of status: With limited exceptions, an individual who has ever engaged in unauthorized employment before or after filing an application for adjustment of status to lawful permanent resident is barred from adjusting status
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