I would think it would be beneficial for my parents to pay off the arrears to slow the repossession of the property.
Maybe this is a stupid question, but if they can pay the arrears, why don't they?
Otherwise...
This really is one where you need to contact a competent solicitor who will advise you.
If the lender has no charge on the property, how can they repossess it?
Presumably they will first have to get a charge on the property? Is that even possible at this stage without the consent of the second borrower?
As I say, your solicitor will have to advise you, but it looks to me as if the bank has an unsecured loan to one of your parents, say your father.
Your father still owes the money. But your mother doesn't.
If that is correct, they can get a judgement for the loan. Then they can secure the judgement on the property and any other property your father has. And then they can seek an order for the repossession of the property. Half the proceeds would go to your mother, and the other half would go to the bank.