I have 3 miniature schnauzers each with different instincts. One will kill a chicken just to kill it, one would play with a chicken til it died, and the other would kill a smaller chicken for the purpose of eating it.
I didn't think my one smaller dog, Zach, would really kill a chicken, but I found out at my sister's house that he would. He is a white schnauzer and to come up the hill to check on him and find him with a blood red mustache and only the neck, head, legs and feathers of my nieces favorite chicken was awful.
My youngest and gentlest dog, Ace, found some baby rabbits under a trailer house. He pulled all three out and played with one until it had died. There was no broken skin or bones, it was just covered in slobber. I raised up the other two until they were old enough to be released. Ace loves to watch the chickens but if they come towards him he will run away. But I am sure if one flutter around just right he would chase it and when he caught it, he would play too hard with it and kill it.
Now, my third schnauzer, Linus, he plain and simple LOVES to hunt! He really likes the critters that have quick movements or are a challenge. I would not trust him out of my sight for 2 seconds!
Ace is the only one of the three I have raised from a pup. The other two have been giving to me from family due to changes in their lives. I love my dogs, so I want to prevent any mishaps, which case they are not left alone with the chickens for any reason.
Now for my cat... I don't know how she understands, but if the critter (be it a mouse, bird, chick....) is in the house and I scold her for glancing at it in a predatory way, she wont mess with it. My parrot has run her off, she won't look at the parakeet, she wouldn't even look at the mouse I had. And when I take these pets outside, the rule still seems to apply. She wont mess with them, won't even look at them. My little bantam Cochin even runs her off. I have never seen her even behave in a predatory way towards any pet that has been in the house when I take it outside. This doesn't mean I would trust her with anything small!! But I am not worried about her killing a chicken or even trying to. She is a very good hunter, she gets mice and birds all the time, use to catch baby rabbits when I lived in AZ.
Any animal that comes from a predatory descendant has got it in them to kill. That is the way they are wired and that wiring, no matter how screwed around, is still there. Although I do believe the herd protector breeds have something in them to allow them to distinguish the difference between family flock and outsiders. But that has a lot to do with breeding, raising and training. I've heard of the Great Pyrenees protecting their family of sheep, yet hunting rabbits and deer to eat. So they have the predator instincts, but they are imprinted on a species to protect and they recognize the difference.
Aren't animals amazing!