Slim, but possible. Say a contractor, in construction, was paying people under the table. He works for a couple that submit his work to their insurance company. The insurance company pays it and write it off to the IRS. The IRS doesn't have any income mentioned from this contractor, they audit everyone. The contractor now gets in trouble by the IRS. He owes lots in back taxes. He needs to write off some expenses to get his taxes reduced. Biggest thing to write off, employee wages. He now reports all of the people that he paid under the table. They are now audited. Being as how they are illegal though, they might just be deported. (I am not sure how the illegal fits)
This happened to my dad. He is an American, was born here, but only had an 8th grade education. So he worked in construction, he was audited for 10 years back taxes when this same scenario happened.
I also worked in a tax office for a while, we had a similar situation. Someone had a lot of kids and wanted to claim them. They filed as self-employeed/independent-something like that. They did a little of everything, cleaned houses, construction, farm work. After they filed income taxes (they kept records of expenses and earnings) several individuals and companies got contacted by the IRS, wanting to know why none of this was claimed before. I left the job before I found out how it turned out, probably a big mess though!!