The death hunters were, as their name explicitly stated, hunters- Predators who tracked down traces of death's influence to destroy, they knew no mercy for their prey, nearly each and everyone of them had either been born to a family in which hunting the dead was a mission since generations, or had one suffered at the cold hands of undeads, and sometimes, both were true.
However, the hunt took its toll eventually, usually, it did not take too long for death hunters to begin to show signs of a certain sort of madness, the most common was memory loss, as they immersed themselves into an endless bloodlust- A never-ending thrill for the hunt- Trying to destroy creatures of eternity, of Oblivion… It often led to them simply forgetting why they had even begun to hunt to begin with, and simply keep going, without understanding why.
The hunt had to go on.