An interesting theme, if not an easy one, I'm finding. Funnily enough, I believe that I saw a theme rather similar to it in a game-development challenge on another forum, years ago. (While I think that I recall the concept that I had for that, I naturally don't intend to use it here.)
I've had a number of ideas thus far; the following are those that have caught my interest:
One idea was to make the player's death a doorway leading to other worlds, and perhaps new incarnations. However, I was troubled by the thought of depicting death in this way: I don't want to depict suicide as something desirable. Further thought suggested that this might be ameliorated by making it advantageous to stay in a given level for as long as may be (perhaps amassing score, items, or character levels), but with death leading on to the next level--the player is thus encouraged to survive, but when death comes it is nevertheless a form of progression, not defeat. I quite like this idea, although it leaves the actual core gameplay somewhat unspecified, which both implies more design work and suggests that death's utility may not be sufficiently central.
Another thought was that the theme doesn't specify that it is the player's death that is useful, only that death be useful. Thus perhaps the player might have access to necromancy or blood magic, allowing them to raise dead enemies or gain power through killing; this might have the additional challenge or requiring that the player perform these actions in specific places. However, another contestant has subsequently settled on something rather similar, and (I feel) rather clever.
Building on that, though, was something somewhat darker: a stealth-based game in which the player takes the role of a cultist--or rather, a series of cultists--attempting to complete a human blood sacrifice in order to summon something horrific. These sacrifices would involve killing someone at each of a series of specific locations--perhaps randomly generated. Further, the good guys know about the sacrifice, and are watching for our cultists, knowing them by sight; if they spot a cultist, they will attack and likely kill him or her. On the other hand, the cultists don't know the good guys, nor where they hide--unless they expose themselves to slay a cultist. There are only so many members in the cult, and losing all of them loses the game. Thus death is useful in two ways: performing the sacrifices advances the game, and dying exposes the good guys involved in that death, allowing the player to more easily spot them the next time.
(I'm currently somewhat leaning towards this idea.)
Last on this list (thus far), I had the idea of some sort of roguelike in which not only is there meta-progression (such as unlocking of items, statistical increases, or mechanical advantages), but the player's corpse appears at an appropriate point in the next run and provides some sort of advantage, allowing the player to press on more effectively once found (perhaps via providing access to an alternate world in which powerups are available, or which lead to the next part of the game). Additionally, the corpses of certain enemies might provide similar advantages. completing the game without a death might be impossible, calling for the player to make at least one brave, doomed run. I somewhat like this idea, but I'm not sure that the roguelike genre is one that I'm well-suited to.
At the least I intend to sleep on these ideas, and may indeed come up with others. Only tomorrow do I intend to select one and build a prototype.
On the technical side, I used some of this time to put together the bare framework in which the game is intended to sit. This largely amounts to a copy of core- and likely-looking- parts from my current main project, placed into a new folder and gutted of most game-specific elements. The new folder was further populated with appropriate empty sub-folders (such as "Music" and "Sound" folders). I also implemented a simple splash-screen class and used that to add the required splash to my game; it could further be used to create additional splashes, and perhaps sub-classed to produce basic cutscenes. There's no gameplay code thus far, but the project runs: it first shows the splash screen, then, after a key-press or mouse-click, fades to a bare-bones main menu with a "new game" button (which does nothing), a "credits" button (which does work, but at the moment shows the credits from my main project), and a "quit" button (which works just as expected! ).