How does Empire of the Sun display the notion of discovering the fragility of life?
The central word in the question is where I am stumped. If you are asking about how the novel expresses the "fragility" of life, I think that this is a prominent idea throughout the novel. The initial descriptions of the morning where the Japanese bomb Shanghai, the forceful and destructive nature of it, set the stage for an exploration that highlights how life, itself, is a malleable property and constantly subject to change and alteration. Jim's life before December 7 and his life after it are completely different and this fragile yet dynamic nature is depicted throughout the novel. When Jim has to deal with death each day in the camps, struggling for survival, struggling to eat, and struggling against others for basic amenities for life, one sees how fragile life is and the struggle to maintain it only highlights such a notion. Throughout his time in the camps, Jim comes perilously close to death, proving how delicate living truly is in a wartime setting.
If the question refers to "frugality," in terms of how life can be lived for very little, I think you would have to examine the work's depiction in Part II of how Jim lives off of very little in terms of food to stay alive. Any life based off of the rationing and limitation of basic needs such as food would constitute as "frugal." This woud represent the essence of a frugal existence where spam represents "the most satisfying of meals."