Where Does 'Dead' Fat Go After a Fat Transfer?

Fat injections or fat grafts transfer fat cells from one area of the body to another. Some of these cells die because not enough oxygen can reach the center of the mass of the cells. We try to inject small amounts in one area for this reason. The cells that do not live get processed by the normal human tissue response of the immune system, including macrophages and lymphocytes. The cells get taken to the liver where they are processed. Infection can occur with any filler, but this is a rare occurrence.

Fat cells are mainly made up of lipids and fat molecules.  Dead fat cells essentially break up by your white cells, a process known as phagocytosis.  Some will also be absorbed into your circulation as lipids or fat molecules.  The lipids will then be transferred through your circulation and further broken down, mainly by your liver. 

You are correct. When we transfer fat to any part of the body, face or buttocks, not all of the fat cells survive. These cells which do not survive will be broken down and their contents (fat-fatty acids and triglycerides) will be absorbed into your blood stream and either taken up by your liver or other cells. There has never been shown to be any harmful effects from this.
As far as getting an infection. You cannot get an infection FROM the dead cells, but there is always the possibility of them getting infected. ie: they will not cause an infection. I have never seen a patient get an infection from fat grafting.