Well, in my experience in SoTx, it's been rich people from Mexico who own businesses here. They hire illegal immigrants and thoroughly rip them off (not just "payroll taxes", BTW) because they know they can. They threaten them with deportation if they say anything. Quite common here, unfortunately.
I think it's even more common, however, to have an under-the-table arrangement. So many of the more well-off people here have live-in maids from Mexico (who are underpaid and are functionally indentured servants) and don't report the payments. Or, subcontractors (painters, roofers, etc) pay illegal immigrants under the table at a below-minimum rate and pocket the profits.
I can't really tell you how it works up North, but I'm going to guess that most illegal immigrants who work there 1)Are paid under the table , 2)Get an Individual Taxpayer Number so they can legitimately pay taxes or 3)Use a SSN that is stolen, from a dead person or just flat out fake. I agree with the sentiment that we have to get serious about enforcement at the employer level. Start randomly auditing companies for compliance with I-9 forms, for one thing. Mandate E-Verify, for another, better option. If we did that, we'd be taking away a big incentive to cross over in the first place.