Ideally it’s just a matter of encouraging workers, competitors, and regular people to report noncompliant employers. Then law enforcement can show up, seize the equipment (possibly putting civil forfeiture to good use), and arrest the employer.

I think people should be allowed to move across borders mostly freely. Whether or not someone is authorized to work is a separate issue. Work permits should be issued at a rate sufficient to maintain support for the population of non-working citizens (those who are too young, too old, or too sick), but not so much as to depress wages.