I have had hundreds of fish in my life and a lot of them got tail injuries, the guy at petco said to clean there tank less often,and they TOTALLY got better,but I don't know about your fish.
Can A Goldfish Fin And Tail Heal?
They tend not to heal fully, the fish will appear to still have the wound, in that it will not grow back to its normal shape. However, if no infection or disease gets into the wound, the fish should be able to live a normal and happy life.
How long can my goldfish live for without a tail?