Divorced, he has no status, no claim. The problem arises when a couple never bothered to divorce.Then the survivor has an automatic right. You can imagine the distress that causes if the deceased had been living with a new partner for many years as man and wife.
In any case, she ought to make a will .Everybody should.Then they appoint suitable people they choose to be executors to take care of the estate and they give directions as to the disposal of everything they own, right down to details. In many cases the intestacy rules produce a result which is far away from what the deceased , or their family,wanted or expected