Upon finishing a novel, or any work where considerable time is spent with one character like a series, there's a grieving period that takes place. It happens to me every time. After months of a character's voice living with you, as a kind of ghost speaking through you, it suddenly goes silent.
I've always looked at characters as these kind of ghosts that the writer helps into existence. Once your task is complete and they've gone, you're left with a bit of an empty feeling. You miss them. Not in an overly depressing way, more like leaving a perfect visit with a good friend that you know you won't see for some time and somewhere in the back of your mind, you know the next time you meet, you might not be as close as you were.
This is the same feeling that drives readers to yearn for sequels, or when a reader really doesn't want a book to end and tries to turn the pages as slowly as possible. As the writer, the creator of these fictions, that feeling can be much more intense as you can imagine. For me, this is why it always means so much when readers say how much a book or character meant to them. It lets you know that didn't let go for nothing - that your character is off making new friends, living within more people, becoming more real with each one.