The Nidbathed of Nidavangr have extra souls on them, giving them an unusual sort of extra lives. If they would die, even through a soul-slaying, one of their scars will disappear and negate the hit. This is sorta like a cross between Luck and Twist Fate.
A Scar Soul only works in a short burst, and cannot correct any structural damage or conditions that make serving the Pretender God impossible. Thus, instakill methods that destroy the body will still kill. For brevity, anything that does 999 or more damage and that isn't negated by being Mindless will still work. Here are some examples:
Getting Scar Souls is a one-time process that happens when one is recruited. They are gone for good if spent. You can control how many Scar Souls a new Nidbathed or Nidhere gets through the strength of Nidavangr's Dominion in Nidavangr's capital. The starting Scar Soul count of a Nidhere always matches the province's Dominion at the time, while that of a Nidbathed is half as many, rounded down.
Undying from a bless will be granted for each life, the hitpoints from it effectively being multiplied for every scar soul. When ending a battle with negative HP and at least one scar soul, a scar soul is lost, but the unit remains alive.
What even ARE Scar Souls? Well, a Nidbathed (or Nidhere) enters the Nidakettil with his friends, gets beaten and cut within an inch of their life by said friends, and watches them all commit suicide out of guilt. The Scar Souls are the souls of his friends, or at least those who managed to bond with the scars they inflicted.
¹ Regarding the last bullet point, there are "drowning" spells that cause drowning but do well under 999 damage. Whether or not these spells ignore Scar Souls needs to be tested.