Their employers pay taxes on their wages through their fake ss numbers. They pay sales tax when they buy things from the store

https://www.irs.gov/individuals/individual-taxpayer-identification-number

An Individual Taxpayer Identification Number (ITIN) is a tax processing number issued by the Internal Revenue Service. The IRS issues ITINs to individuals who are required to have a U.S. taxpayer identification number but who do not have, and are not eligible to obtain, a Social Security number (SSN) from the Social Security Administration (SSA).

Perhaps not income taxes, but maybe taxes on goods and services, property taxes, etc? Can’t say for certain though.

In my opinion the costs are much higher to not integrate new peoples. Undocumented Immigrants provide a lot of the ingredients but take none of the pie. I’m not going to sit here and say cheap labor is acceptable, but there is a point where you have to admit we wouldn’t have nearly as many workers in less desirable employment fields if not for immigrants, even if wages were higher. They are also on average younger than an aging local population.