I think this is one of those ideations everyone has, not morbid, just from the dark part of normal. Sort of like suicide, almost everyone thinks "what would they do if I turned my own hand?"
If the children are young, I would say definitely to support them, and if they are adult you discuss it with them. The answer to this question depends on the situation. If it is a deceased ex-spouse, you may want/need closure.
I always attend a funeral to support the family that is left behind, or if it was someone close to me, to have the closure as well as seeing the family.
