I have a friend who keeps a free ranging flock and has a pit bull terrier, a griffon terrier mix and a Chihuahua. The larger two are fantastic with her flock and are very protective of them...the Chihuahua on the other hand, chases them relentlessly any chance he gets and tries to attack them even though they're three times his size. She and her family do their best to make sure he doesn't get out of the house unless it's straight to the dogs' fenced area but once in a while he'll slip out the front door and he's so little and quick, he's not easy to catch.
That's what happened with us. The doxie managed to sneak out of the house- we KNEW he'd go after the littles- he'd try to snap them out of our hands - so he was being leashed to go out. No one knows how ge got out that day. Once they got bigger, he was ok- it was the younger bantams without mamas he got. But he's gone. Took him to a small dog rescue. I was SOOOOO mad. So mad.
My cairn terrier leaves them along. So does my rough coat Jack Russell and my border collies. The GS mix got a single bird. We trained; he left them alone. He was doing well {although barking at horses and chasing the baby cows, so it was prolly a matter of time} until he decided to go after my cats. But ya. Sometimes the littles are the worst ones because they have been bred to go after vermin.