I would guess that yes they can, and you'd have no way of knowing aside from one trick.
When you open a closed chest, bookcase, anything it makes a sound (turn up your volume and listen). If a chest is stuck open we can see its stuck open but I am pretty sure it no longer makes the chest opening sound when you access it... the same goes for bookcases etc. So.... if you were to access a bookcase etc. and no sound happens... it would be "stuck open".
EDIT because of not knowing visually I would recommend storing valuable items in chests only. Not bookcases
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