In the first instance the Debt does not die with the person. Debt is the first thing paid for after legitimate funeral expenses. If someone has, for ease and arguments sake, £1000 assets. If they leave 50% each to their two children or £500 each. The children would get whatever is left after debts and expenses. £1000 less £500 funeral expenses = £500 less £250 charge on house = £250 less £200 other debt = £50. The kids will be lucky to see £25 each.
How is the house mortgaged and owned. She must have an interest it if there are charges from her debts on it.