I live in the country and we deal with loose dogs all the time. The idea people get that "I can drop this unwanted. undisciplined, and/or unhealthy dog off in the country and someone will take it in" is prevalant and dangerous.
There is, the best I can figure out, a sign up at the road in front of my place that says (written in dog) "Come on up, she's a sucker." I get about 10 - 12 drop offs a year and at least one or two whole litter of puppies that wander up into my front yard. I don't have livestock, but I'm in a livestock raising area. A dog dropped off at a farm or ranch gets a completely different reception than one does at my house. They have penned/fenced animals that are expensive, are their source of income and are dependent on them for protection. Those people must react decisively toward stray dogs.
If these dogs come up to my place, I have the luxury of fencing them, cleaning them up, medicating them (somewhat), feeding them to get them healthy again and interacting with them. Then I can tie a bow around their necks, run a free ad for them and find them a home. I've come across a few in the last 17 years that I wouldn't try to find new homes for. If a dog has been too badly abused or mis-treated that they are always suspicious of people, I won't try to find them a home because I don't feel that dog would be trustworthy around children. I also cannot and will not keep every un-placeable dog that comes up. So, some owner has lazily put their responsibilities off on me.
I say I have that luxury because I have a place I can observe these dogs before I get too close to them, I don't have small children in the house to be endangered, and I don't have livestock. If any of those facts were different I wouldn't end up with Mel's halfway house for abandoned dogs. I have learned through the years, it takes a lot for a single dog to turn mean. You put three dogs together running wild and you have a dangerous menace, not pets that need re-homing. Some dogs have been so abused they cannot adjust to people and aren't safe. Some dogs have been abused terribly (I've treated the wounds from some horrible things people do to their dogs) and NEVER give up on people. I have to admit I've kept a couple of those dogs through the years, I just couldn't make myself take a chance on them being treated that way again.
The biggest problem with domesticated dogs "going bad" and running wild and becoming dangerous is people. They won't train their dogs, they abuse or neglect the dogs, and they don't take the responsibility to do what's necessary for the dogs. They drop them off instead of finding them a home or shelter. They think it's cute to teach the puppy to "attack" and then are horrified when the 80 pound dog thinks it's still ok. It is infuriating.
I'm not saying that dogs have rights over people, I'm saying that when one person abdicates their responsibility, the responsibility doesn't go away. It simply must be borne by the next person who comes along. Regardless of whether it is a neighbor's pet creating danger and terrorizing the neighborhood or Fifi who gets heartworms and the owner is too lousy to get them treated or make the tough decision to put them down. The next person who comes in contact with that dog must protect their own children, animals or property, or it may be some sucker like me who will find their dog a home.
The problem is the same, there's a lot of people out there who are too weak to stand up and make the grown-up decisions and take care of their responsibilities, be those responsibilities pets, children, family, or personal. That is at the crux of a lot of problems in this country. Mental children playing grown-up.