What a sad situation! They are responsible for their dog, though. One time many years ago, I was driving down the street at dusk and hit a HUGE black lab! I pulled over and was in tears. My children were in the car and were crying (the boys were 2 and 5 at the time). It was hard for all of us. Anyway, I got out of the car and the poor dog was still alive but very badly mangled/hurt. It was a country road where the houses are about 50 yards apart (not quite country, but not quite in town either, but a semirural area). The woman came out and started screaming at me for hitting her dog. The man across the street had been outside watering his lawn and was a postman, still in uniform, obviously had just gotten home from work. He runs out into the street and shakes his hand in the woman's face and says, "Stop yelling at that poor woman! This is on YOU! Everyone on this street has told you and TOLD YOU that if your dog doesn't stop darting out into the road after cars, one of these days he's going to get hit. And today was just his lucky F@*#ing day, wasn't it? Keep your dog in your own yard or don't cry when it gets hit. YOU are responsible for your animal and you know it." She ran in to call the cops. I waited, cops came (this was 20 years ago when they would still come when you called). Both officers told the woman that her animal was in violation of the county's animal code wherein all dogs must be either fenced in or, if out, on a leash or tie-out that does not allow the animal to be beyond the owner's control. She begged and pleaded with these cops to cite me, and they told her over and over that she should have kept her dog in her yard, that dogs that chase cars ALWAYS eventually get hit.
Animal Control had to come out and take the poor thing to the pound to put it down. It did not die, but it had non-recoverable injuries. I will never forget it, but now I'm left with this memory because this woman didn't keep her dog in her yard. Your neighbors bear that same responsibility.
If she didn't call the cops, maybe it's time you did... if nothing else, for the safety of that poor animal that they can't seem to be responsible enough to keep in their own yard.