When my aunt died I notified the housing department the following day and asked if any rent was owed on her council bungalow. They told me she was on full housing benefit and the rent was up to date, however as executor of her estate I’ve since received a bill for more than £225 for the period from her death to the date I handed the keys back some three weeks later.
The council is obliged to stop housing benefit from the date of death, since entitlement to it relies on residency and, to put it bluntly, if your aunt is no longer there she no longer qualifies. It’s quite common for local authorities to ask the deceased’s estate to pay the rent until the house is vacated. If your aunt had no money the council will probably write off the debt.