We had this come up a couple of times recently in 401(k) plans. The employees who were fired for using someone else's SSN were completely unresponsive to attempts to contact them about their distributions. Both had less than $5,000 vested balances. The auto rollover provider for the plans, Millennium Trust, said they can not accept funds for someone without a correct SSN. The plans also contain a provision that forfeits the balances of missing participants who are due an involuntary distribution. Normally, the auto-rollover provisions would apply before the missing participant provision. But, with an auto-rollover being impossible, the missing participant provision applied. Both participants' balances were forfeited. If they show up to claim their benefits and can prove they were the person who earned the benefits, the forfeited balance will be reinstated. The plans also have a provision that if the missing participant has not been located by the time the plan terminates, the forfeiture becomes irrevocable.
If your document has a similar provision, it may help you resolve the situation. If nothing else, it may convince the PBGC to make it their problem.
Good luck.