Same thing that happens if they are living with someone else and they die of natural causes. If there is a will it is disposed of according to that, if there is no will your local jurisdictions laws on inheritance apply (in common law countries, generally meaning assets are distributed among deceadent's family, which may require a sale in order to split the value). If there are no heirs, then it generally goes to the state to dispose of however it wishes.
Of course this assumes that the estate can pay off its debts, or the house will need to be used to pay them off.