As long as the base of the fin is left intact without deterioration, then your fish should regrow his tail. However, you must act fast to determine what is causing this erosion !
First, describe the fin to me. Does it have a cottony growth at the tip of the deteriorated area ?
Also, please answer these questions for me so that I can help diagnose this problem :
1.) What are your water parameters ? Ammonia, nitrIte, and pH are needed.
2.) How long has it been since your last water change ? At that time, did you thoroughly vacuum your substrate ?
3.) Other tank inhabitants.
4.) Size of tank and type of filtration.
5.) History of this tank ... any history of illness ? Any other fish in this tank have the same symptoms ?
If I can have a bigger picture of what is going on in your tank and with your fish I can better help you !