She says her old body dies but it doesn't appear to leave its corpse anywhere. Is that a glitch?

Nope. Unfortunately, the Adra Dragon just dissappears afterwards

The game isn't very nice for the greedy or soft-hearted. I can think of one instance where you don't get anything for killing a person.

 

Actually, I think the rule of thumb is: whichever takes more effort, yields the higher reward in Pillars of Eternity. If you can kill someone straight away or do a quest for him, (The ogre in Endless Paths) more reward. If you can talk someone out of something, or kill him, killing may give you more. (Sky Dragon).