I am not absolutely clear what you mean by "there was no knowledge of the debt before the death". I am therefore to assume that the Executor to the Will had no prior knowledge of the existence of the debt, but one would presume that the deceased did have full knowledge of a debt incurred during his/her lifetime. If my assumptions are correct then, yes, the Estate is liable for the debt incurred. I cannot think of any reason why the deceased would have had no knowledge of debt in the first instance in any event.