Easily accomplished.
Pass a new Federal law requiring all employers to use E-Verify for all employees and contractors. Any company then found to be hiring illegals, the CEO would be liable for jail time of 1 month per illegal employee found to be working for them.
The employment prospects for illegals would dry up in a few weeks and they could then turn themselves in and leave voluntarily for a chance to return, if they pass a background check, can prove they’ve never received any kind of means tested assistance and contribute meaningfully to the economy. If they’re just here to take jobs away from teenagers and ur domestic welfare population, they can’t come back.
That would have to be those found with illegals working for them after e-verify fingered them: for many employers it is considered lawful or discriminatory to question or doubt the fake IDs that illegals give them.