This is an extension rule (Ex) and is not part of the official rules.
When a character is killed, though they are mechanically dead, they may save vs. death once, any time up to and including the 1 turn downtime at the end of the encounter. If they pass, they may speak for up to 1 minute. After that, they are gone.
No spellcasting, device use, ability use, movement, combat, or anything other than speaking is possible.
Final Words can be used in order to ask for divine intervention. They can even be used for this purpose if the character is unconscious when they die.1)