I have had 2 fish have that have lost their tails completely. One was due to being stuck in a rock, and the other was a clean bite. Both fish were smaller than a red tail, but both fully recovered and grew a tail back.
What I did in both cases was a hospital tank with a 50 percent water change daily. I added salt to the tank. I also did a methylene blue dip for about 30 seconds, twice daily for the first few days. After that, I just left it up to clean water, salt, and a completely stress free environment. I kept light off the hospital tank as well.
Fish can be very resilient, but you have to give them the best environment you can to support a potential recovery.