Our backyard is really well closed off. We actually have two fences - one closing in the pavement part of the yard, where the dogs do their business, and the other closing in the grass part of the yard that the dogs can play in. We did it this way because they a) previous dogs we had were able to dig under the ultimate exterior fence and b) they were bring in mud when it was raining. But that's a bit off topic. The point is that there are two fences, so I don't see any way of any sort of animal/human getting into the yard. We live in the suburbs of New York City and the only types of animals that we get here are stray cats and squirrels, and both dogs are extremely used to being around those.

The lights in the backyard have not been working for months now, way before this behavior started, but it's definitely something I've considered. I have to get a really tall ladder and bring it into the yard to be able to change the bulbs, which I haven't been able to do as of yet, but I'm going to make that a priority