I was thinking about offering to help look for holes, we've had to do it to keep our birds in our yard and if it helps protect the flock...
The dog is a Jack Russell, meaning he either dug a hole or will dig a hole to get out. However, he did give us a flyer for a place that sells birds this late in the season, and has offered to pay for 4 birds. We do free range our birds, and this is a risk we have had to deal with many times, but we can't bring ourselves to sentence these birds to a life in a cage / fenced off yard. He lives several doors down, and i'm honestly surprised that the dog ran this far from home.
The hatchery he has offered has some fairly pricey birds, and he has been very clear that he would only replace the birds his dog killed, so I think it would be best not to push my luck by making any list...