None that I'm aware of. But I have had a the falcons/cooper hawks shadow me and use my pressure on the quail to create an opening for them to take advantage of. I've also used them to my advantage to finding a covey. Watch where cooper's hawks go. If you see them bouncing around on top of cover, bushes, etc. they've probably located some birds for you.
I’ve had this happen 2 times in the same area quail hunting. The first time was the most impressive I shot the quail it hit the ground bounced and the falcon snatched it on the bounce before it hit the ground again. Me and my dad looked at each other and both had to make sure the other person seen it. The other time shot a quail and didn’t have a dog with us, and the falcon came and stole it before we could get to the opposite side of the berry vines we were hunting
I say if the hawk gets it it doesn't count against your limit because you never possessed it. Your dog on the other hand is an extension of you and you should have control over him. So any birds Fido eats counts against the limit.
I've had vultures take dove that I set aside and walked away from. Those count against my limit because I had possession before the birds got them.
Once, I had a smallish raptor, (falcon?), munch on a dove I'd shot and took a few minutes to pick up.
The best one was when I was hunting with my daughter and I was the bird dog. She dropped a dove and I went around the trees in the wash to get it and had to call her over to see this. A snake had poked its head thru a forked branch to snatch the bird, when it backed out it would end up with a mouth full of feathers. It was fun to watch with a mouth full of feathers and nothing to help get them out. WE watched, laughed, then shooed the snake from the bird and went our way.
I got some butterfly larve every year and my second graders would watch them develop and turn into butterflies. One year as I set them free out on the playground while my class watched, a bird swooped down and grabbed one of them in mid-air. Half my little 8 year old girls started crying, but most of the boys thought it was cool.