In general terms, while I do not know the meaning of "undeath", except as describing the state of walking corpses, I can relate it in the sense of what Carlos Casteneda prescribes as telling one's self frequently "I am a being that is going to die."
Or, put another way in his conception, one is "using death as an advisor."
How that breaks down is basically recognizing one's impending death and cultivating an energetic attitude towards life that transcends (or strips down) the normal perceptions of existence into a more fundamental "seeing" reality directly. He painted these things in colorful terms with lots of psychedelic adventure effects, but that's just telling a story.
Warrior cultures throughout history have and still do practice a frame of mind as considering one's self already dead, especially before entering battle. This may not have been a general ethic shared by all in the fight, as survival is a hard motivator under fire, but to abandon one's self in the face of the enemy or in the conditions of brutal endurance - or even existential despair - seems to have its appeal.
I've heard "die in every moment" as a value expressed from various angles. I am not sure if this was originated in Buddhism or if it just a mystically oriented thought that naturally pops up as a matter of course. But if we consider our lives as a constant "bundle of perceptions" that will apparently terminate at some point, the only certainty being that we will perish just as we had been born, then the attitude proceeded could be a source of calm acquiescence and resignation often needed for meditative peace.
In Platonism, the "Art of Dying" was taught I think in the above sense for the sake of embracing the eternal world as opposed to the changing world of particular things with all its divisive unpleasantness. Here it is seen as a purification, hopefully to avoid reincarnation which results from addiction to the particulars. I believe this is rooted in Pythagoreanism, where the idea of transmigration is a kind of punishment. Of course, all these ideas can be found in Indian based philosophy-religions, but for all I know they go back to Stone Age where some shaman recognized the soul of a deceased friend in the body of a dog or mammoth and was moved to pity.
