One of the cap experts may correct me, but I believe the only way they can re-sign Rudy would be through the non-Bird exception. That would allow them to give him a contract starting at 120% of his current salary. They could give him up to a four year contract under the exception, with a max 5% increase per year. His cap hold for next year will automatically be 120% of this year's salary. Or at least that's how I remember it.
I believe that's the only way for them to get him re-signed. I've said before, I think him leaving would be a disaster for this team - especially since they wouldn't be able to spend that money for someone no on an exception. I know he's getting older and has had injury problems, but I think they will do everything they can to try to keep him. I think that means something like 3/$40M, and hope he signs. Maybe the third is only partially guaranteed.
He only played 57 games last year. He's already played 57 this year, and there are still 11 games to go. So even if he gets a few nights off before the end of the regular season, he'll finish with around 65 games, which is more than Nephew will play this year. If he plays that many the next two years, it means that he's healthy enough to do what they need.