You should probably have taken this question to a biochemistry teacher, or better yet, someone who specializes in human metabolism.
Yes, there are fat soluble toxins that will be released when fats are metabolized. There are also fat soluble vitamins, like A, D, E, and K which will be released. The problem isn't the fat ... it's the toxic compounds that have come into your body from your diet and the environment at large.
Apart from that, your body oxidizes fats every time your insulin levels revert to baseline. Barring some disease state, like metabolic syndrome and the attendant hyperinsulinemia, at the very least, you will spend about half of every day metabolizing fats. This happens on a nightly basis, about 3-5 after your last meal, and until you eat again the following morning. This state, that of fat burning, is actually your normal state. It is only very recently in history that we have had such regular access to food and have come to spend most of our waking time accumulating fat rather than oxidizing it.
P.S. Bonus marks for the palindrome.