It's a complex one.
less calories in + more calories spent = weight loss
Not exactly.
less calories in + more calories spent = changes to the body's composition.
The theory is right. It takes 3,500 calories to burn a pound of fat. But eating 3500 calories less, doesn't mean you are going to lose a pound of fat. It all depends.
For one reason, this is based on your Basal metabolic rate being static, which it isn't. It moves up and down, so who knows how much you are burning throughout the day.
Many people who do a lot of cardio whilst on a VLCD, find they are too tired to move around much the rest of the day, and do less fidgeting etc. Basically, they can often 'play dead' after it..thus slowing the metabolic rate.
Also if you are burning so much, and not taking in very little, the metabolic rate can crash big time and you are more likely to go into the starvation mode that people dread.
There's also more chance of lean mass loss and water retention, neither which show on the scales.
Evidently of these problems don't happen if you do resistance exercise which appears to keep the metabolic rate more stable and reduces the chance of lean loss.
Of course, exercise is important, but when on a VLCD, if you aren't used to doing a lot, then don't do a lot
A walk, a swim..blah, for the health benefits, not for the results on the scales.
Once you get moving up the plans, you will have more calories for your body to play with without going into shock
BUT, much depends on what sort of exercise, the intensity, the duration, what you are used to etc.