I have four neon tetras, but I bought one that has a broken fin. None of the others seem to be attacking/harming him. The only difference between him and the others is that he sometimes swims on his side. Will this fin possibly grow back eventually as long as nothing bites him?
I will preface this answer with I know nothing about this particular fish. However, quick research reveals that they're extremely peaceful towards one another but easily bullied by aggressive tank-mates. So, it should recover if no one in your tank bothers it; assuming it doesn't appear to be diseased and your tank parameters are optimum.
It may be wise to quarantine the fish for a short while, as it recovers, especially if you have any strong currents in the tank or if it seems to have difficulty getting food.