"Lucky" fin. One of Betta's fin is significantly smaller than the other

[jvivet]

Hi everyone! So for a late birthday present i was given a "baby" betta from petco/petsmart in a tiny tiny 40 oz little container. Apparently she had spent as much as a week or so in the tank before given to me and another day while i searched for any sort of tank i could get. No filter, no heater. Today was the first day i was really able sit down and just observe my fish and i noticed that one of her fins in the front (the ventral fin i believe?) is only a stub when compared to the other. She is a deep blue veil tail female, with red starting to appear on the upper portion of her anal fin(not sure if this is a natural coloring has she has started to get more vibrant in her new tank) Her one full ventral fin is mostly red as is her stub both tipped with white. I was wondering what could have happened that caused this? Is it treatable and will it negatively effect her health from here on out? thanks everybody.