OK, what we have from the original is
Let's see. Here's my first attempt, but I'm sure you'll have some good ideas.
While some undead dragon slayers rise from the dead through the sheer force of their burning hatred of dragonkind, most are heros of dragon-fighting cults given a semblance of life through necromancy. They are all united in their desire to see all dragons --- and those who would aid dragons --- dead. Undead dragon slayers will keep company with any others who are seek to kill dragons, and they are often accompanied by skeleton warriors as help in their endeavors. Almost perversely, undead dragon slayers can sometimes be found in the presence of dracoliches or other undead dragons; as undead, a dracolich doesn't arouse the slayer's ire, and territorial dracoliches can use undead dragon slayers to drive other dragons out of their territories.