I have personally seen this. One SSN having 20+ individuals working in 10+ states at the same time. Clearly fraud but the US Citizen that is the victim of identity theft is not offered any help. Left subject to audits from the IRS. SSA will not help or issue a new number. They know where the thieves are but refuse to take action. That would be another Executive Order I would support. Mobilize law enforcement to round up these thieves.
And when the original (real) owner of the SSN applies for benefits?
Does s/he get all that paid-in money or does s/he get accused of fraud?
I can guess the most likely outcome...