Any research that I have read indicates that vitamin deficiency has everything to do with poor diets and not due to the storage of fat-soluble vitamins. If you think about it, everyone stores fat soluble vitamins in fat tissue. Given the same amount of vitamins, the same amount will be stored in obese people and regular-sized people. Fat soluble vitamin deficiencies occur in people whose fat absorption or intake is abnormal -- those with Bariatric surgery will face issues because the part of the intestine responsible for fat absorbtion is compromised. Those on very low fat diets don't have the fat available to absorb the vitamins.
Once the fat globule absorbs the vitamin, it travels through the lymphatic system of the small intestines and into the general blood circulation within the body. These fat soluble vitamins, especially vitamins A and E, are then stored in body tissues.
Fat soluble vitamins, once they have been stored in tissues in the body, tend to remain there. This means that if a person takes in too much of a fat soluble vitamin, over time they can have too much of that vitamin present in their body, a potentially dangerous condition called hypervitaminosis (literally, too much vitamin in the body).
This is a whole lot different from the concept that fat soluble vitamins aren't available for use because they are socked away in the fat. What actually happens is that, despite body weight, the fat absorbs the vitamin and transports it for use. Where the issue lies is if you take TOO MUCH of the vitamin, regardless of your body weight. Any excess in vitamin will THEN be stored in your body fat (even if you are thin). THIS can result in hypervitaminosis
. So the body hangs on to the vitamin and stores it for FUTURE USE. The vitamins are still available, they've just been put aside until blood levels trigger the body to release them. They are still available for use. And from what I can see, the research out there indicating otherwise is tied specifically to sites that are selling vitamin supplements or dietary programs or books on metabolism.
Your second question is: what happens when fat is metabolized? IF you have excess vitamins stored in your fat cells they will be released and excreted. But you need to recognize a few issues, as this is a bit complex.
Vitamins A, D, and K are stored in the liver, and Vitamin E is stored throughout the body's fatty tissues. During weight loss, body fat is metabolized and not your liver.
So (in the absence of disease) IF you have excess vitamins stored, you will have symptoms of hypervitaminosis long before it is released in your body. For example, vitamin A is stored in your liver: excess vitamin A will damage your liver and you will have the associated signs and symptoms. This, though, is actually quite rare, and reported cases of hepatotoxicity (liver disease) are limited to arctic explorers who consumed seal and polar bear livers which are extremely high in pure vitamin A. Our usual source of vitamin A is from plants high in beta-carotene, such as carrots and peppers (bright orange and yellow ones!). But the body converts only as much beta-carotene into Vitamin A as needed, making this a safe source of vitamin A. The liver is also primarily responsible for the release of the other fat-soluble vitamins (D, E and K) because as blood levels of these vitamins decrease, the liver is activated to start metabolizing its own fat stores (and adipose tissue in response to vitamin E) to release the appropriate amount of vitamin. So when you talk about hypervitaminosis, the problem is that the stored excess vitamin causes disease, NOT that the release of vitamin excess causes disease
The general consensus that I see is that there is no issue with respect to fat-soluble vitamin release during weight loss, as with a balanced, healthy, unsupplemented diet, the amounts of vitamins stored aren't particularly huge. IF you are mega-dosing because you think you are deficient in these vitamins, I would see a doctor to get assessed, because these vitamins accumulate in the body regardless of body weight, and too much will cause trouble, diet and weight notwithstanding.