They absolutely can. Done it to mine before. They climb over kill the bird usually by bitting the neck then carry it over. Sometimes there can be little to no evidence. That's why I said get a camera.Could they run off with a duck without leaving any trace behind? The only way to get in is to dig under the barn or climb an 8 foot high fence. There aren't any large holes under the barn as far as I know. The only way to get in is to climb the fence.