Back in the bad days of Thatcher and Norman LeMont (old badger chancellor himself) negative equity blighted those who had taken out mortgages, often for the full value of their property (in some cases 110% even!), and then when the property bubble burst, people could end up owing more to the bank than the house was actually worth. So properties would be ceased and then sold on, often at auctions.
If these people were able to recover to the point of wanting to buy a new house, they probably will have taken out debt consolidation loans to get to that stage.
If house owners already have a bad credit history, but need money to purchase something, they will search for bad credit remortgages.