legally as a spouse you are not personally liable provided your name wasnt on the agreement as for example with a joint bank account -or failure to pay a direct debit or bill which your name is on - but the estate of the person who died is liable , so when the estate is sorted out, the outstanding amount is taken out before the person who inherits it receives the rest.
If for example you are the person applying for probate and also the beneficiary the same still applys, although you may choose too pay if its a small amount and you want to clear it up, you cant be forced to pay it out of your personal assetts, they have to apply for payment from the estate for the money to come out of the estate.
If there is no estate they cant then demand the spouse (or other next of kin to pay at all) except in certain circumstances
- they might be able to demand half an outstanding amount if it was a joint account or a shared agreement that you were paying out too with both names on it, as the legal assumption would be that you were paying half so you were jointly liable for the payment, and that is the case even if the whole payment was coming directly from the personal account of the person who died, the other person on the agreement would still be liable for half.
So what should have happened was that the meters should have been read and the account with the electricity company closed with an invoice for any outstanding amounts submitted to the estate administrator to be paid from the estate - then a new account from the day of that meter reading being opened starting from the meter reading of that day - just as if some-one moved house - they wouldnt charge the new resident (new account holder) for the old residents past account holders) outstanding bill.