Death isn't alive, but neither is it dead. It simply is. It takes those who have died and ferries them to the afterlife they are tied to. It has even done this to supposed immortal beings.
Immortality is not invincibility.
There are souls that elude it for a time, either through magic, soul anchoring, or any other variety of factors. Eventually, they found their way into the listless, wispy presence of death. Reunited with their loved ones, taken from others. Death has always been seen as a being of evil by the living due to these things, but it does not embody such concepts, being detached entirely from such mortal empathies.
However, there is a large group of souls that defy the basic rules of life and death. Souls that it can't grasp, and many of these souls purposefully harass and annoy Death as they come through. And then they come through again. And again. And again somehow. They are linked to a world that somehow predates existence and defies the concepts of chaos and order themselves.
Follow Death in this short tale as it rips its nonexistent hair out when it deals with members of the World of Illogic when they 'expire' through external factors.