My kids have a dresser and somehow they have managed to pull the sides partially off. (In all fairness, it could have simply been an age issue – the sides were originally stapled on and it is 20 years old). I've tried using a couple of screws to hold it together, but they aren't managing to hold it as tightly as I would like.
The design is pretty basic. There is an interior structure which allows drawers to move in, but the sides actually hold the channels for the drawers.