Deer and such will not fight unless there are no options and it has the necessary energy and verve. Apart from immediate physical entrapment, they do not realize that they likely have no options in the long run (pun fully intended). So they run and keep running until they fall into the trough of low energy.

Not to mention, the first weapons would have been far more basic and require closer range than a bow and arrow or a throwing spear. So, to your point, early humans would have had to have taken advantage of the sickly or exhausted in order to avoid injury. With exhaustion occurring as a byproduct of the hunt, it would have been an “accidental” discovery.