I'll say you've been beyond patient. It would be hard to kill such a sweet dog, especially when it sounds like that happened through ignorance and mismanagement...they basically pointed the dog to your chickens, prob let the dog out to potty and its gone. I'm sure you know it will be back. Just catch the dog and rehome it for them...to the animal shelter...in the next state...the ground is too hard to dig in this time of year. I only have a small run, could never keep all the chickens in it...just chicks and broodies for a little while...so I really depend on my mutts to run predators off.