I would seriously doubt this exists.
An empty fat cell is a fat cell that has given up its contents in the line of duty ... that is, during a period of energy scarcity, this valiant cell sacrificed it's contents for the good of tissues at large, and you expect to repay it by killing it?
Apoptosis of empty fat cells is not an evolutionarily stable strategy. You need empty fat cells because you need excess storage capacity to act as a sink for excess energy when the environment is kind enough to serve it up to you. Without excess capacity, you would need the ability to grow new fat cells very quickly on demand, something which is rather more expensive metabolically than keeping empty fat cells around.
Moreover, if prolonged weight loss induced fat cell apoptosis, then over a long enough time frame, you would wind up with zero fat cells which means that precisely at a point in time when you desperately needed the ability to store energy. Further, yo-yo diets would logically conclude with the hapless dieter in possession of a few grotesquely enlarged fat cells. Neither of these outcomes is observed in real life.
As a final point, fat cells never get "empty" per se. Rather, they contain very little triglycerides relative to the "full" version of themselves.