There are three categories of NPCs as far as dying is concerned:
First, there are jarls (nobles), important villains, dragons, and other upper-class types. Those start dying at -1 hp and are dead at minus their Constitution.
Second, there are karls (free commoners), intelligent non-humanoids (other than elementals, constructs, and undead) and intelligent named humanoids. Those start dying at -1 hp and are dead at minus half their Constitution.
Finally there are thralls, anything with an Intelligence score of two or less, elementals, constructs, undead, and unnamed intelligent humanoids. Those die immediately when their hit points drop below zero. Note that constructs and undead actually die AT zero hit points; the other types of being listed here can be staggered but will die at -1 hp.
Creatures with special rules that require some specific point of death, like wild boars, die at that point instead of the point stated above; typically this is minus their Constitution score.
These rules are for NPCs only; PCs have a larger buffer as described in the character generation section.