I know this controversial and not everyone will agree with me. But I think in an urban setting, your attracting other peoples pets by having chickens. People and pets live too close together. It's almost like having a female dog in heat in your yard and killing all the male dogs that come around. Or putting out bird feeders and killing the birds that try to eat the seed. You might need to consider keeping your female dog, bird seed and chickens protected and then everybody gets to live.They are doing what they do by instinct. I live in the city, I feel like it's my fault if a predator gets to my chickens because I didn't protect them. I would never let my dog run free, I have baby gates and doors to ensure my dogs don't bolt out the door when the garage door goes up. But none of us are perfect. I feed a feral cat because I want a cat around outside to help with rodent control. I trapped her and got her fixed. I didn't bring her here. She was born under a neighbors outside shed. There have been no more kittens since I got her, her mother and her sister fixed. No one wins if some one traps her and kills her. More feral cats will come that have not be vaccinated or sterilized. IMO if you have chickens in the city, your yard should be dog proof and your coop raccoon, possum, cat and rat proof. You shouldn't have to trap raccoons, possums or cats unless they become relentless because they have been successful in getting to the chickens at some point.
I know my avatar is a lady with a rifle ready to protect her chickens, but she's in the country, and I just like the picture.
In my mind an agricultural setting is different. Farm dogs are held to a different standard, and people live farther apart and fenced yards are not realistic. If the dogs and cats can't stay on their own property and they kill chickens, their days should be numbered and the SSS is justified IMO.