Right, its still on him because he didnt keep his account current per GB's Terms of Service, thus creating his own problem.
He cant really check with ups though, they'll only assist the shipper. Only the shipper can file a loss claim, etc.
To finalize this you should get with ups for verification that it was delivered to the address listed in his GB account just to cover yourself. Maybe someone did in fact sign for it anyway.
IIRC, they'll have the receiver sign for stuff if someone actually answers the door, whether its required or not.
Go check with them, you might get lucky on the signature issue.