Hi Amy- the reason I asked who was the executor is that I think it's the executor's responsibility to ensure all debts of the estate are paid and the net estate is distributed in accordance with the will.
Anyway, in the circumstances if the council agreed a final settelemnt in 2010 and has now discovered money is due from 2008, I think the council may write the debt off if the executor presses for that.
But if you can afford the money maybe for peace of mind you should just agree to pay it between you.