This is what is taught in medical school about the effect of low-calorie dieting on metabolism. This is why 'diets FAIL, why most dieters regain the weight they lose. This is why weight management is about long-term, healthy, living, lifestyle, NOT going on a diet.
When you do not eat for a day or any other prolonged period, your body produces the energy it needs to live and move by "eating" your muscles instead. Muscle weighs more than fat, so when you step on the scale, you will see that you have lost weight.
When you are not consuming adequate nutrition, minerals, and vitamins, your body leaches these from your lean tissue body mass, effectively reducing even your bode density. 'Osteoporosis, the thinning of the bones, is often called, 'the slimmers disease,' for a good reason. The human body needs calcium and minerals for the function of it are vital organs including the heart and if insufficient nutrition is consumed the body will draw nourishment from the bones to protect the vital organs. When calories are reduced the quality of those calories is more important than ever before.
Consider, that muscle takes the most energy for your body to maintain. A person with a lot of muscle mass burns more calories per day than a similarly built person who has less muscle, even if both are just sitting on the couch watching TV.
So, when someone stops fasting, he or she will have lost weight because they have lost muscle mass. However, his or her body will now burn fewer calories per day than it did before they started fasting. If that person were to start eating again as they did before the fast, he or she would now gain weight, whereas, before the fast, they broke even and neither gained or lost.
It is quite possible that the same is true for when you eat an extremely low amount of calories per day. Your body needs energy to keep moving and living. It is not getting that energy from food, so it burns up some muscle because muscle a) provides more nutrients than fat, and b) requires more energy to maintain, energy that your body no longer has.
The belief that your body goes into starvation mode, is a simplistic way of explaining the lowering effect on your metabolism of low-calorie diets. Your body does not think "oh, no food, better lower my metabolism for a while." Your body is a machine really; it does not think much of anything at all. Eating too little, however, does lower your metabolism because your body is eating up its muscle mass. This is not a temporary change, though, as the words "starvation mode" may lead you to believe. The lowering of your metabolic rate will be permanent until you exercise to build back the muscle you have lost.