Peeves was never a person, therefore it never had a job of work assigned to them.
JKR spoke to this issue directly on the FAQ on her old website
Q : Peeves chews gum, how can he when he is a ghost? (Nearly Headless Nick can't eat).
A : Peeves isn't a ghost; he was never a living person. He is an indestructible spirit of chaos, and solid enough to unscrew
chandeliers, throw walking sticks and, yes, chew gum.
She's also provided some extra clarity in a Leaky Cauldron interview in 2005
ES: Why does Dumbledore allow Peeves to stay in the castle?
JKR: Can't get him out.
ES: He's Dumbledore, he can do anything!
JKR: No, no no no no. Peeves is like dry rot. You can try and eradicate it. It comes with the building. You’re stuck. If you've got
Peeves you're stuck.
ES: But Peeves answers to Dumbledore -
JKR: Yeah. I see Peeves as like a severe plumbing problem in a very old building, and Dumbledore is slightly better with the spanner
than most people, so he can maybe make it function better for a few
weeks. Then it’s going to start leaking again. Would you want Peeves
MA: If I was Harry I might, but as a reader I enjoy him. I enjoyed him most when he started obeying Fred and George at the end of
JKR: Yeah, that was fun. I enjoyed that. That was satisfying. [Laughter.]