What one of the four big ideas in biology does Stiff: The Curious Lives of Human Cadavers address?

Well, I assume you mean the big ideas of an AP Biology course; the answer I would choose is Systems or Energy, although the case could be made for all of them. 

I say systems because death involves the entire body, top to bottom. Most of the chapters were concerned with how people use bodies. The first few chapters were about dissection and organ harvesting, like how systems of the body are separated at death for use in testing and research. Chapter three was about how the systems decompose after death; little had anything to do with the other topics of information or evolution. Medicinal uses of body parts and forensic research all seemed to fit the topic of systems.

I would say energy because the topic is death itself. The research on the mass of the soul and literal soul-searching was very concerned with how energy is stored in the body. In the second to last chapter, Roach considers using corpses as fertilizers, composts, and lamp fuel as an alternative to traditional fuels, and even before that discuses cannibalism throughout the world.