Actually, what happened to Jim is irrelevant because -- like many of the events in Donnie Darko -- the whole bit about Donnie heroically revealing Jim as a child molester is a fantasy in Donnie's mind.
As I explained in answer to another question about Donnie Darkoanother question about Donnie Darko, the movie shows the main character Donnie developing schizophrenia. The schizophrenia causes Donnie to believe he is at the center of a time-travel adventure that just might save the universe -- and the movie depicts Donnie's madness as it appears to him -- as if it was reality.
The scenes with Donnie's psychiatrist are the biggest clues to this -- she has some idea of what is going on with him. And another key piece of evidence is that in a deleted scene (availble on the DVD) Donnie has a conversation with his father where Donnie, in a moment of self-awareness, says "Dad, I'm crazy."
