Lord of The Rings: Fellowship of The Ring - Frodo's Shirt
When Frodo awakes in the bed in Rivendell, Frodo's shirt is open and the sheet low down on the bed in the first shot, and then his shirts closed and the sheet pulled substantially higher in the next shot.
I don't think he closes his shirt at all. What you're seeing is the bandage around his shoulder, showing under his shirt. Besides, Eru is right. Just because the camera is not on the character does not mean they're not doing something, such as buttoning a shirt or moving covers.