Dangit, tried to edit the comment to amend my theory and managed to delete it instead. :/ Edited version was meant to read:

I got the impression the Barely Breathing Deer was a real deer, but empty. It "caught" the BBD, “ate” its soul or conciseness or whatever, and was waiting to use it as a lure to ambush the humans.

That’s why it was just off the Human Game Trail, that’s why it was pulled so close up against a tree it had a hoof on the trunk, and that’s why when Grandad tried to startle it with a clap, water fell off the leaves and branches directly over its head in perfect time with the head turning.

Whatever the fuck is hunting them, I don’t think it’s shapeshifting. I think it’s using the empty bodies of the other things it’s caught like decoys, and turning the deers head required some kind of movement on its part, like controlling a large marionette. But they didn’t go up to the deer, they went wide around it - so it couldn’t Death From Above them.

Wonder if it uses the deer as lures for other things beyond humans, like bears or mountain lions.