As an aside, I’ve seen this happen elsewhere as well. Classic play for wage theft. When I was working as a bartender in London to make ends meet, I had a coworker from Mexico on an expired visa. Great guy and the most hardworking. Well won’t you guess it, guy got picked up by immigration authority on payday.
Would probably be far more effective. Punish the employer for not taking reasonable checks. Are they paying tax correctly?