Interesting that Goldman doesn't have good enough background checks (or any background check?) to catch fake SS numbers. The securities industry is supposed to fingerprint and check any candidate who would be licensed, which a securities salesperson generally would be.
It was not easy to check SS numbers back then. She joined the firm in 2005. The systems that verifies them today is recent ( http://en.wikipedia.org/wiki/E-Verify ). It did not really start working well until 2007. http://www.uscis.gov/e-verify
I'm also a little surprised that you can work and pay payroll taxes to an invalid SSN. Shouldn't that raise a red flag when someone pays payroll taxes to an invalid SSN, or when the name of the employee doesn't match the name on the SSN? Doesn't the social security administration notice that and notify ADP / the employer? Not just to combat fraud but also to uncover and fix honest mistakes when someone flips a digit in an SSN?