I'm not sure anything will happen. It would be best if he were not even mentioned, and the character thrown into the bin. As it stands, the only living witness to actually see how Murphy died is Harry. Harry, who was going to have a warrant put out on him. If Rudolph and whomever has been pulling his strings stir the pot, Harry would be put under the microscope again. It would be easier for the story if Rudolph was now background, because if we keep focusing on him, Jim would have a tough time actually focusing on the enemies he needs to deal with to wrap things up.
I could sort of see Rudy showing back up in a future book, only as a broken, failed no one who has self-destructed
hard after this. Butters knows the truth (even if he didn't see it) and he's still well thought of by the CPD so all he has to do is (accidentally, since he's a Knight now) reveal what happened to a single cop and Rudy's immediately becomes (even more) persona non grata. Or Rudy could just self-destruct due to guilt and his brief return could be a "Redemption Equals Death" moment...
But overall, I do think this is the last we've see of him...