Resolved Question: How would this debt of a deceased be handled?

Husband dies with only an underwater house as probatable assets. He has other assets, but all contain beneficiaries and can quickly be transferred to the beneficiary’s ownership. The mortgage is in the sole name of deceased. If no one steps forward to probate the house, would the bank be able to find the beneficiaries (how?) and if so would the bank sue the estate or just foreclose and walk. Obviously there is no concern about credit. If the bank sued the estate, how would they try to retrieve the already distributed assets?
Bob, I trying to say that no one is stepping up to be the administrator. NO ONE is volunteering for this position.