Ill be honest and say most people who grapple in my experience are constantly carrying some type of injury. I had a torn Rotator cuff which was a nightmare, multiple broken ribs which are probably the worst because you have to sit out completely. My most serious were ruptured discs in my neck but I have nearly a full recovery at this stage.
Fingers are a constant problem breaks, dislocations or just plain sore.
Right now I'm in pretty good health bar a lingering knee problem as well as the usual overall soreness.
It all depends on how you manage them but BJJ is highly addictive and its not easy to sit out for any length of time.
When on injured I turn up for class anyway just to watch and take mental notes but by the end of the night I'm usually on the mets for a roll anyway.
Depending on how bad I'm hurt of course, I just can't watch everyone roll/spar and not want to jump in.