It's not that complicated. If you burn up more calories than you take in, fat will be used as fuel and the person's weight is reduced.
Naturally, the body fights potential fat loss with a million and one brilliant strategies (some of them physiological, and others psychological) but at the end of the day, the human body is not a perpetual motion machine, and the weight will eventually come off. Maybe not a quickly as we'd like it to, but there is only one possible outcome when more energy is burned than is taken in, i.e., weight loss.