If they got a mortgage, they'll be on record at the courthouse as being the current owner.
Property taxes are assesed to whoever holds the title to the property. The mortgage holders have a claim to the title, but have to foreclose to get it.
If they can't foreclose, the residents are left with title, but the record of the unpaid mortgage will probably be enough to prevent anyone wanting to buy it from ever getting title insurance. The current owners can still live there, but they're still responsible for the property taxes, and they'll never be able to sell it in the open market.
They can file a motion to quiet title and get the title cleared, especially true now the court has ruled in their favor.