I get property and sales taxes, but how are they paying income tax? Shouldn’t they have a SSN for that?
That's a part of why there was a lot of hubub about ICE searching the IRS's databases for potential targets. There are a lot of people who are probably working in the US paying income taxes without authorization to stay or work in the US. The IRS generally doesn't care about your immigration status, it just cares about collecting taxes.
An illegal / undocumented worker working a standard W-2 paycheck job is going to have taxes withheld and sent in by the employer, even if they never file their own tax return.