^^^ They have fake SSNs and income taxes are taken out under that SSN. I've heard of people receiving their annual social security statements to find out that someone was working under their same SSN. Fake social security cards can be purchased on the black market, from what I'm told. That is why it is pretty hard to hold employers of illegals responsible since most illegal workers look like they have legitimate paperwork.
ETA: Even for illegal immigrants who aren't using fake SSNs, many still pay taxes under ITINs, I guess. I was looking for something else and found
this article on how the "economic stimulus" plan is being tailored to make sure the illegals who filed taxes under ITINs don't get the refunds. A more explanatory article on the ITIN practice can be found
here.