Okay... first the short version, since I blather on below... what happens to the unused fat is, it's stored in your fat cells for later use.

my understanding on a standard, mixed diet is that if somebody is eating say 2000 calories a day, and in maintenance, neither losing or gaining, and say their eating 80 grams of fat a day--then they'll burn about 40 grams of that dietary fat, and 40 grams of body fat. The unaccounted for 40 grams of dietary fat goes into storage.

The same will apply to somebody on a very high fat diet. Some of the fat you eat, your body will use for energy, with heart and muscle etc. getting fat from chylomicrons, the lipoprotein recently absorbed dietary fat is transported in. Beyond heart and muscle a major "etc." is fat tissue, lots of the fat from the diet will find its way into your fat cells, this is true even when you're losing weight. There it gets mixed in with fat you already have stored, which is way more than you've eaten, and then later when you're fasting, fat is released from that general store. I haven't seen anything on how much fat goes directly to providing energy on the way in, on a ketogenic diet, versus what goes into storage, whether it's about equal like in that mixed diet example, but it's liable to be something similar, but with higher numbers since fat is a higher percentage of daily energy.

I would try eating a bit more protein and lifting weights or some other sort of resistance training.