When somebody dies their liability ceases. The account balance (and only that) in their name is the responsibility of the person's estate and that will be administered by somebody (or several people in tandem). The liability from that death going forward is a separate entity in my mind. Hence a new account with the supplier. In essence its similar to the fact that the deceased's bank accounts are frozen and an executor/administrator is best advised to open a new account in the title of "executor in the estate of X" to deal with receipt and payments of money. It probably will be the responsibility of the same people. But where any debit or credit on the deceased's account will be included in the Estate figures, which might have to be reported for IHT or probate purposes depending on value and other factors, the ongoing energy usage is not and its solely a matter for the Executor/administrator to deal with in their task of distributing the residue to the beneficiaries.
And yes a change of supplier is possible, subject to normal limitations.