Do you think all those painters, landscapers, day laborers, housekeepers, babysitters are paying taxes?
In the commercial construction industry it isn't all that surprising to have an ICE raid on subcontractors occur and find fellows that have valid SSN and Driver's Licenses and yet find out they are illegal aliens.
You can get the proper documentation, in good faith, on an I-9, pay in benefits against an SSN and after a year or two find out that the employee is actually illegal.
The Social Security Administration NEVER sends back any money. You might hear they have a problem getting a number and name to match up, but they always keep the money.