Think of it like this: when fat is absorbed by the body, it is always in the body until it is burned - no matter where in the body it is. Adipose tissues function is to store the fat, which is does quite well. When the body is in 'fat balance' the release of fat from adipose equals the amount taken up (from lipoproteins). Some of the fat released from adipose makes it to the liver, where it goes into the synthesis of VLDL. The faster the adipose releases fat, the quicker VLDL is formed. VLDL is only released once it is completely formed. The VLDL travel in the blood vessels around the body where cells can use them to take up fat (including adipose tissue). A cell takes up the fat and can oxidise it for fuel/energy.
If the person is in negative fat balance, adipose releases more fatty acids than it takes up - the person loses fat. So, it is important to consider both the uptake and release of fat from adipose tissue when talking about fat loss. Supplements that just increase fat breakdown move the fats into the blood, where it is likely to come straight back (same as inflammation).
Cells can use free fatty acids for fuel. The problem is that little regulation occurs as to which cells receive the fat. Normally, lipoprotein lipase (enzyme is spoke of earlier) is expressed on cells with a high metabolism, so they can most of the fats. Free fatty acids can just move into any cell. Once inside, it can even produce toxic substances under the right conditions.
Adipose tissue inflammation can be described in two ways: 1. oversupply of fats which hypertrophy adipose cells to the point where they become de-regulated. 2. infiltration of macrophages followed by activation to their inflammatory state (think low grade whole body inflammatory state). The exact causes can be numerous, but it definitely is not a good thing.