Employers should be able to go online securely to a government Web sight and be able to verify social security numbers. When they run a check a picture of the person with that social security number should come up. Then it would be much easier for an employer to know if the number provide is bogus or not.
The only requirement of the employer is to run the check and heed the results.
I am an employer.
What do you do with a mom and pop store that may hire someone to do something, and THAT someone hires an illegal? There are a lot of ifs and buts for this.