What happens to the fat after liposuction?

Which fat? If you mean the fat that is removed, it is usually discarded like other medical waste. If you mean the fat that remains on your body after liposuction, it continues to behave like fat, getting larger if you eat more calories than you burn and shrink if you burn more calories than you eat.
Remove & incinerate. Unlike fight club the fat is not used for soap. In the future it has the potential to be a great source for stem cells. Currently it is disposed of as medical waste (incinerated). Dead fat which is left behind inside the body is typically resorbed by your body.
Permanent fat loss. Liposuction removes some, not all, of the fat cells. The remaining fat cells can enlarge if the calories consumed and exercise regimen are such postoperatively that there is still a positive caloric intake. More calories in than needed equal fat accumulation, and the fat will go somewhat in the remaining cells in the treated area as well as other areas that didn't undergo liposuction.
Liposuctioned fat... ...doesn't typically return to the treated area, even if you gain a little weight.
Nothing. Liposuction removes some of the fatty layer directly under the skin- the remaining fat cells can still enlarge if you gain weight and shrink if you lose weight. After lipo, you may notice a weight gain differently ( in a different area).
Gone forever. The fat cells are permanently removed never to come back. But if you gain weight the remaining fat cells will enlarge .
Fat cells in liposuc. Fat cells and their attached progenitor cells removed by liposuction are permanently gone. In the event of poor diet and exercise conditions, addition of weight and percent body fat can go up due to other cells with the abiity to metabolically store lipid in the fat cells. Secondary weight gain outside of 'genetic" determined areas typically responds better to diet/exercise than primary areas.
Permanent removal. The fat that is removed is permanently gone. The remaining fat cells (not all are removed in any area) may still get larger with weight gain, but the proportions should be much better.
It's gone! The fat cells that are removed during liposuction do not come back. Consequently, their removal by liposuction will give a permanent change in contour. Your new shape will remain essentially unchanged. However, if you gain a significant amount of weight, the remaining fat cells in those areas can enlarge. This can give you a larger version of the form and contour that you had after liposuction.