This is my nightmare. I imagine I'd for once in my life go for a run and this would happen to me. A guy was out on a run one day and realized a few minutes into his run that he was in fact being followed by an animal. Don't worry, tho. It wasn't a scary animal like a cougar or bear. It was far more cuter than that! he was being followed by deer! You can see them prancing around behind him in the video below.
Still not going to get me to for a run, tho. I'll stick to the gym.