In this case, the bank is just saying, “You’re no longer our customer,” and sending him a cashier’s check for the balance / value of his accounts.
In other cases, where the authorities have seized the accounts, the assets are frozen. The bank will turn it over to the authorities (federal, state, whatever) where the monies will generally be kept in an interest-bearing account that keeps track with inflation or similar but otherwise remain inaccessible to the original owner until the legal matters are resolved.
The only time, setting aside simple banking errors, the Bank would keep it is if the Bank is owed money anyway. LIke say, Jones had a huge set of outstanding loans he’d refused to pay. The Bank would simply take funds from the deposit acocunts and use them to pay down the loan(s).