I didn't see any rot.. any chance that the others could of eaten the fins?
How often and what % of water do they change per week? Goldfish needs extra filtration, and plenty of water changes because of the amount of ammonia they produce - this could of been ammonia burning/poisoning.
Usually 2 filters with 1-2 50% water changes per week (including vacuuming the substrate) is needed with goldfish.. but I didn't see any blackened edges on the fins/body which would indicate fin rot..
Breeder so I have too many to count and too many named to list here!