Science magazine has an article on the death of one of Yellowstone's wolves. In this case, the radio-tagged alpha female of a pack that had 95% of its territory inside of the park, was shot less than a mile from the border, and it appears had no history of predating on commercial livestock.
The way Science tells it, they don't appear to have thought carefully enough about the hunt. While it'd be damn near to impossible to get commercial farmers in that part of the US to accept regularly losing livestock to wolf packs, there's a difference between allowing hunting to control wolves that hang around farmer's land and wolves that prey on elks. In this case, it doesn't appear to have occurred to them that rather than scout around the extensive livestock areas for problem wolves, the hunters would just go to where they wait for the elk to leave the park and gun them down and do the same with the wolves.
In the meantime, a wolfpack that was not affecting livestock, was a subject of intense research, and was a signature animal of the park, has been effectively wiped out.