Yes. I used to raise goats. we had a mixed herd of Nigerian dwarfs, some La Manchas and some mini manchas.
I had two GSDs at the time, one I still have, the other has passed. The one who is gone now was a confirmed killer of wild animals and livestock. I even got him to the point that he could carefully walk through the pastures of adult bucks with me.
My two victory moments with that dog were when baby kids crawled out of the little places I didn't know they could escape from and popped out in front of him and when I told him to leave it, he did. That's why I trained so hard, because I didn't want my dog imprisoned in the house and I knew eventually someone would pop out and either he'd rip their throat out or I would have trained him to the point that he wouldn't. I succeeded.
My other dog would only chase and would not follow through. But even chasing can kill. I stopped her from chasing fairly easily and she and my lab mix were the only ones allowed to actually bum around with me while I did chores and just freely mingle with the goats.
The killer dog never had liberty like that because it was still there, would always be there, and could be triggered. I even made sure to put 2x4 hole fencing on the fences that faced our yard so that goats could not stick heads or noses through, he would totally have grabbed any body part he could grab.
I sold some goats to a lady who had two GSDs and they were not very well trained or supervised. Their got into her pen and chewed up the buck I sold her pretty bad. He lived, she got rid of the dogs rather than train or contain them better.
I think my killer dog was unusual. He didn't go for legs or back ends he went straight to the throat for the kill shot, he was like a lion. He wore a basket muzzle during training with livestock for a LOOONG time until I had proofed and proofed and proofed