Yes, they do! I just explained it to you. They are issued ITINs and work with that number to register their earning with the IRS. Where do you think the stats for income revenue from illegal immigrants come from? You keep talking about a felony being in the states illegally when it's actually a civil issue and as I said before the wheels of the federal government turn very slowly so these illegals requesting refugee status or are trying to become legal have to work. Of course, some of them work under the table but that isn't anything exclusive to illegal immigrants. Many have let their visas lapse, some are in the US on student visas and need to work. There's lots of reasons why people in the US whether they are bona fide citizens or not require an ITIN.
The Individual Taxpayer Identification Number (ITIN) is a tax processing number issued by the IRS to ensure that people pay taxes even if they do not have a Social Security number (SSN).
www.americanimmigrationcouncil.org