The correct answer is that fat is converted to carbon dioxide and water. You exhale the carbon dioxide and the water mixes into your circulation until it’s lost as urine or sweat.
If you lose 10kg of fat, precisely 8.4kg comes out through your lungs and the remaining 1.6kg turns into water. In other words, nearly all the weight we lose is exhaled.
This surprises just about everyone, but actually, almost everything we eat comes back out via the lungs. Every carbohydrate you digest and nearly all the fats are converted to carbon dioxide and water. The same goes for alcohol.
Protein shares the same fate, except for the small part that turns into urea and other solids, which you excrete as urine.
The only thing in food that makes it to your colon undigested and intact is dietary fiber (think corn). Everything else you swallow is absorbed into your bloodstream and organs and, after that, it’s not going anywhere until you’ve vaporized it.