It is probably a known issue. Vicious neighbor dog making a beeline to attack his old dog every time it gets out. He is trying to kill it or give it a pavlovian conditioning to run away from this place every time it gets out. I had a neighbor whose wire-haired terrier would get out and go after anything that moved. One day it attacked our 14 year old honey beagle bad. The neighbor came and got their dog and apologized. I told him I will shoot his dog if it comes on our property again. 2 days later it was back and I shot it. The neighbor came and screamed at me for killing his dog. I told him he was the one who killed his dog because he didn't train it properly and I hated him for making me kill a dog. I was 13. I am now 58 and I still feel bad for that dog and I still hate that piece of shit neighbor.

I don't think the owner of these two dogs would have reacted that way if the other dog wasn't a threat.