I have been hesitating to post a reply on this thread because its been 20 years since I've taken cell biology. However, here is the theory that I would suggest.
1. There are structures in cells that require a water solution -> Nucleus, Mitochondria, ribosomes, etc. The stored lipids form a mycelle (lipids have one non-polar side and one polar side) that will vary in size based on storage level.
2. Cell Membranes are for the most part static structures. In order for them to grow, you must add lipids to the lipid bilayer (more to the outside, than the inside) as well as protein anchors.
3. Adipose cells do not generally trigger mitosis as they reach a certain size.
Given these general assumptions, my guess is that as fat is removed, water is used to keep the cell structurally sound. At a certain trigger point, one of 3 things happen: The cell canibalizes the cell membrane and shrinks, the cell becomes similar to a phagocyte (meaning it drops volume but retains surface area), or it dies decreasing the number of adipose cells. This study suggests it could be any of them.