The way it works in the states is, if you're well fixed the federal government will eventually bail you out and tax the working poor to found the bail out. I don't know how things work in the UK.
When a bank gets into trouble, for whatever reason, some kind of arrangement is normally set up--sometimes it involves governmental agencies, sometimes not--for said bank to be taken over by another bank. If they didn't do that, as you point out, there would be nobody to pursue the borrowers.
The government is usually motivated to get every last dime they can from the borrowers, so they don't have to come up with as much to bail out the gamblers who took the bank over the cliff in the first place.