General Discussion

If you're in the country and aren't documented, you're deportable on that basis. They show you're not authorized for entry or continued residence, done and dusted.

If you're an employer hiring somebody authorized, the law looks simple enough:

It is unlawful for a person or other entity—
(A)to hire, or to recruit or refer for a fee, for employment in the United States an alien knowing the alien is an unauthorized alien (as defined in subsection (h)(3)) with respect to such employment, or
(B)
(i)to hire for employment in the United States an individual without complying with the requirements of subsection (b) or (ii) if the person or entity is an agricultural association, agricultural employer, or farm labor contractor (as defined in section 1802 of title 29), to hire, or to recruit or refer for a fee, for employment in the United States an individual without complying with the requirements of subsection (b).

Then it goes all pearshaped. It seems still crystal clear at the beginning, though:

(i)In general
If any employer that is a member of an association hires for employment in the United States an individual and relies upon the provisions of subparagraph (A) to comply with the requirements of subsection (b) and the individual is an alien not authorized to work in the United States, then for the purposes of paragraph (1)(A), subject to clause (ii), the employer shall be presumed to have known at the time of hiring or afterward that the individual was an alien not authorized to work in the United States.

(ii)Rebuttal of presumption
The presumption established by clause (i) may be rebutted by the employer only through the presentation of clear and convincing evidence that the employer did not know (and could not reasonably have known) that the individual at the time of hiring or afterward was an alien not authorized to work in the United States.

But what constitutes evidence? Attestation of examination of documents. So that

Such attestation may be manifested by either a hand-written or an electronic signature. A person or entity has complied with the requirement of this paragraph with respect to examination of a document if the document reasonably appears on its face to be genuine. If an individual provides a document or combination of documents that reasonably appears on its face to be genuine and that is sufficient to meet the requirements of the first sentence of this paragraph, nothing in this paragraph shall be construed as requiring the person or entity to solicit the production of any other document or as requiring the individual to produce such another document.

They give you fake ID and it appears to be genuine upon examination, you're clear. (There's a bit more to it than that--SS card, for example, but those have usually been easy to fake ... Or get false documentation issued. Now, proving that the documentation is false from the SS-side of things and from the employer side. Been there, done that, but not recently. Still, if the ID's obviously fake to a cop that doesn't mean it's obviously fake to the verification officer at the company. Back when I did this, the Clinton-era civil rights guidance also provided a teddy-bear cholla of problems: If you suspect that the person's ID is fake because they're Latino or some other accented person's, you'd better perform the same rigor of investigation for everybody else's, otherwise you're violating their civil rights.) This makes that presumption of knowledge easy to overturn and makes the cases hard to prosecute, because it's employee person by person.

That's the way the law was understood back then and it's how the law's apparently still understood. Both "round'em up and deport them immediately" and "round them up and toss them in jail" ignore Constitutional rights, but toss rotten tomatoes from different sides.