I think you missed alot somewhere along the line. Here coyotes follow deer around ( not in chase ) until they are herded up. When the rest of the pack follows up they circle the yarded up deer. 1 will go into the yard and drive the others out. Then the other coyotes pursue trying to make a kill, as the deer make a brake for it. If you have never seen or heard about it in your area that is not my fault. But, here in the Northeast it is normal coyote tacticts. As you can tell from that photo they are not always sick and weak deer either.