The biological processes that occur in a corpse are well-defined, and are more or less undirected chemical reactions. Rigor mortis, for instance, occurs as a result of the depletion of ATP--the cell's main source of energy--which stops being regenerated upon death. Individual cells may remain alive after death, but without breathing and circulation, will not remain alive for long.
I really don't want to get too complicated here; self-directed (self-sustaining) biological processes are what I was referring to.
Undirected? How are they any less directed than any other chemical process? They are also no less "self-sustaining" than any other process. They are sustained just as long as necessary to accomplish their purpose, just like every other chemical process.