Strays.
A problem in many rural areas. Both cats & dogs.
If feral,, sadly,, they can be a problem.
I spend a lot of time in the woods,, and I've seen cats & dogs. Most cats get a pass,, because I do not know if they are just someone's wandering pet. I'd feel real bad if a child has a beloved pet that just doing what comes naturally, wandering around exploring,, and I were to kill it. Dogs or cats.
Dogs,, I also try to judge their behavior.
I've had people bring dogs from out of state,, and release them to run deer in our woods. (Illegal too!) That happens,, the dogs get killed. By the same token,, many years ago,, I had a dog come to my deer stand, and lay down. She was lost. She found me. She had a collar, and I was easily able to get her to come with me to my truck. I called the owner, and the lady was not only overjoyed, she was surprised. That dog was a rescue,, and didn't take to too many men. She had wandered away from the owner's boyfriend as he was hiking in our area. That dog was a perfect little lady in my home, around my pets, and was very loved by her owner.
Dogs I see chasing deer,, get shot.
And I have enough coyotes around to where any cats that wander & stay around,, are allowed to live. I haven't had any issues with excessive loss of any other wildlife. Heck, I have video of a bobcat inside my barn chasing a rat.
Remove one type of predator, and a different predator will take it's place.
As for the picture provided by the OP,, those two dogs would be killed if on my place. Obviously doing no good.
I have rescued many animals over the years on my property. I've also had to kill several as well. It all depends upon the attitude and actions of the animal.