Just clean water with a water conditioner will regrow the best and the safest. You should treat him for anything unless he has fin rot or something. I would give him some more stuff in his tank and keep his water extra clean. That is really all you can do with tail biters. You have to love them as is and keep them clean and give them lots to explore. Salt won't help the fin growth.
I agree what everyone wrote. Also i think in your situation he is stress because of parasites so he might even bite the tail because of that. For now is most important to get rid of the parasites sense it can be fatal. And then like everyone wrote with clean water hopefully he will get better. Sometimes i think you can't stop it...but you need to keep it from being infected.
After you done treating him with aq salt and then you need to wait make sure he don't have it … And when you sure he is cleared you can add plants, or ''toys'' such as a bottle cap lid, or ping pong ball..good food..
Now i just was thinking. jazzy has plant in the tank. Most plant not tolerant to the salt treatment. Than i know any plant can carry disease. So if fish has external parasites than I think plant might carry it too. juzzy i would really quarantine the plant until you really sure your fish doesn't have parasites. And while you quarantine it for about 2 weeks if plant carry parasites it simply will die without host.
Also if you have cave. I would also wash it every time when you make his daily water changes for aq salt treatment. I also would air dry it for 4 hrs (not really sure how long though) before putting it back. This way you sure that parasites died. I would really do it especially that cave has ridges. Actually i am not sure if it really would be batter to take the cave out. Or it enough just to clean and air dry.