Coup De Grace: If a player has been incapacitated (paralyzed, unconscious, Sleeping, etc.) This does not mean the character is dead. A player will not have to make a fortitude save. If the damage is more than your hit points and the amount of hit points you can go below 0 your character is dead.
Untimely Critical hit: If a player is one shotted by a lucky critical strike (this includes loss of their hit points below 0) the character can not be revived for that combat, and a healing check or spell must be cast on the player before combat is resolved or the character is dead. This rule is still up to the DM’s discretion however if other circumstances were involved.
Brutal Hit: If the player gets hit with an attack that would take it below 0 and far enough to kill a character the player can opt to be at half of their negative allowed hit points and are bleeding out. This can only happen once a session, and as above if circumstances or recurring behavior causes an abuse of this rule it will be taken away as an option for that player.