I don't have this problem. If I love the story, the world, and the characters, I can't wait to have the whole thing complete. It's not an end, but a beginning, because I know there will be many rereadings.
It is sad when a beloved author dies, because I know there will be no new stories of any kind. Or if I discover an author who is already dead, and I know there are only a set number of stories before I run out of new ones to read. But the end of a series, that doesn't bother me. I want that final book now, thank you very much.