Death & Death Saving Throws

Whenever a character's HP is reduced to 0, they are not necessarily killed. Instead (under normal circumstances), they're Knocked Out. If they're reduced to exactly 0 HP, then they remain Stabilized, but if below 0 HP, but above their Death Threshold, they start Dying. A Stabilized character simply remains unconscious until their HP is brought above 0. A dying character must make a Death saving throw every turn, rolling a d100.
When making a Death saving throw, three possible outcomes are possible. If the character rolls a value greater than or equal to [100 - Constitution - Spirit - Luck], they immediately Stabilize. If they roll a value less than or equal to [10 - (Constitution + Spirit + Luck) ÷ 30], they instantly die (this can be reduced to 0). Finally, if they roll in between these values, they lose 1 HP.
A character normally can have their HP reduced to a negative number before actually dying; this is their Death Threshold. By default, it is equal to [0 - Constitution]. If the character's HP is less than 1 but greater than or equal to their Death Threshold value, they remain Knocked Out, but if it is reduced to less than their Death Threshold, they truly die. Characters that are Stabilized and suffer any amount of damage that doesn't kill them begin Dying; conversely, Dying characters that receive any amount of healing that doesn't restore them to at least 1 HP become Stabilized. Some debuffs may alter this.
Characters with Regeneration alter their KO mechanics. If they have Slow Regeneration, then they instead recover 1 HP if they Stabilize or every turn while Stabilized, lose 1 HP instead of instantly dying if they roll low, or otherwise gain or lose nothing; their Death Thresholds are also lowered to [0 - Constitution - Spirit - Luck]. Characters with Fast Regeneration recover their normal amount of HP while Stabilized, 1 HP if between the two values, and simply recover no HP if they roll low; their Death Thresholds become infinite, meaning no amount of damage can kill them while KO'd, though they still have a Death Threshold of [0 - Constitution - Spirit - Luck]. Many types of Slow Regeneration and all types of Fast Regeneration have a "suppressing" effect, which neutralizes it for 1 turn after being exposed to it. For example, most vampires have Fast Regeneration, but if exposed to any amount of Radiant/Light or Radiant/Fire damage, it is neutralized. While it's neutralized, a creature with Regeneration can be killed if their HP is brought below their Death Threshold. For any undead that do not have Regeneration, if their HP is reduced to below 0, they are "killed," but can be reanimated if their bodies are not destroyed.
If a character is killed due to ordinary damage, their bodies remain intact, and they can be revived by most means. Spells like Resuscitate and Flame of Life can resurrect a character who has been dead no more than 1 or 3 rounds, respectively. Characters that have been dead longer, but no more than 1 day, can be resurrected by the Resurrection spell; this limit can be extended if the body is subjected to a Preservation spell, extending the time limit out to a week. If dead longer than 7 days but less than 10, then the Reconstruct Body spell may be attempted at the site of the character's death, but this spell randomly makes a new body; a male Human may be brought back as a female Elf, though the spell favors a body similar to the one the target last died in. If the victim died with a soulstone on them, then Resurrection and Reconstruct Body have no time limit. If not, and if more than 10 days have passed, only a True Resurrection spell can revive them, unless their soul has been purified and reincarnated; typically, this will not happen any sooner than 100 years after their death. In all cases, undead cannot be resurrected this way, and mechanical creatures have no time limits other than the reincarnation limit. Anyone who either died of old age, cancer, or a naturally-occurring disease cannot be revived. If the dead person doesn't wish to return, they also cannot be revived. In any case where a Sacred Diamond is needed for a spell's material component, a soulstone with the person's soul may be used in place of a single diamond. If the creature had no soul or soul-like equivalent, or the soul is unreachable or destroyed, it cannot be revived.
If the source of damage that kills a character is severe enough, then the character's body will be too damaged for anything other than Reconstruct Body or True Resurrection to revive them. Generally, if a person suffers damage that reduces them to twice their Death Thresold, their body is damaged beyond normal revival; if they suffer more than twice their max HP in damage, their body is blown to smithereens. If killed by a successful Coup de Grace, their body is destroyed beyond normal revival. If a spell's effects would destroy the body (such as the Disintegrate spell), or would corrupt the body with undeath, then only Reconstruct Body or True Resurrection can resurrect them.
There is said to be a forbidden Coven spell that can bring back someone from anything, provided their soul is available...