Not only that, but you have to produce certain docs to fill out the I-9 portion of your pre-employment paperwork. One of those docs is proof of citizenship or national or resident alien proof.
Some employers ignore this and don't bother to check.
Fine them. Into bankruptcy.
I agree with everything you said. But you left out a huge violation in which Employee A produces a valid appearing proof of citizenship (belonging to someone else) and presenting it as his own. He signs the W-9 to certify the tax id and name.
One year later, he presents a completely different social security card with a completely different name. It could even be a woman's name. The employer is prohibited by law from pursuing or rejecting this. The employer also is getting dinged $50 a pop for each taxpayer ID filed that doesn't match the IRS records.
This is a bigger and more prevalent problem than people understand.
The illegal is making free use of the identity and is also affecting the real owner's tax responsibility and retirement benefits. Not to mention the havoc that can be created if the illegal uses that tax id to "open" a new credit card.