I agree!! He had a bad start to life, then found a friend in your son, and when your son is gone Woddy gets upset.

Like the others said, I would make sure the door is closed when your son is not home.
Another thing you could try is have your son sleep in the same T-Shirt for a few nights, then when your son is not home for the night, let Woody sleep with his shirt with his scent on it. This way Woody would feel like he's still home!
(I would still keep his bedroom door closed)