In the Mess and the majority of the Puzzlebox, death is at most an inconvenience. At regular intervals of Time, the matter encryption system built into most of Puzzlebox's ecosystem takes a full backup of every willing resident. If the resident's body or mind ceases to function, the instantiator system will simply replace it. If their body is merely damaged, the instantiators will restore and repair all lost functions. Puzzlebox is more discerning, however, about "fixing" Its inhabitants minds -- perhaps It realizes that "broken" is too subjective of a definition for it to intervene?
The backup system has an opt-out system. Some residents, known around the Mess as "single-lifers," choose to limit themselves to a single biological existence, without hope of restoration if they suffer harm through accident or malice. This, perhaps, is the ultimate sign of devotion to an art or philosophy, and perhaps such people should be pitied intensely... or taken very, very seriously... or both.
Few people want to create a character with the intention of seeing their mortal demise. However, there's a lot of emotional power and impact in playing one that does. Whether through accident, old age, or actual malice, character death is always a profound turning point in any storyline, and Puzzlebox should be no exception to the rule.
Note also that natural lifespan doesn't preclude immortality, and not all immortals are ageless. Imagine a creature that cycles from birth/hatching/spawn through maturity to death -- and then starts the process over again. Or reverses it, oscillating endlessly from youth to age, age to youth...
Mortality can be taken to an absolute extreme, as well... what if a creature is born within Puzzlebox, who has exactly one day to live?