I leave my cam's out all yr, 24/7365, and have for about 20 yrs now or more!
and like you I too have an injured doe/yearling, showed up second week of buck season, holding its front leg up, no gun shot or wound can be seen, and leg is being HELD up by the poor thing now ever since, we had a real bad ice storm just before it showed up and I think it fell on the ice and damaged its leg
never easy seeing them be this way
all the more so when you see the other deer pick on it, as they know its not right
I had hopes that a hunter would have got it to save ti from a harder life, but so far its been hanging in there
have seen many 3 legged one's last a few yrs too, had one that went for like 4 yrs before a local guy targeted it as a goal, and took all season to get it, but he did!
gather a 3 legged deer that lives that long was pretty smart one, minus the original injury, but had to learn to get by on 3 and avoid hunters and coyotes and such!