I live in a rural area too and its a pretty big problem here; although its mostly cats. I've taken in many abandoned animals...
Eddie was dumped. Before he made his way to my house, my neighbor's said that they had seen him hanging around close to our road for a few days. He finally made his way to my house and barked at my door, wanting in. It was in the middle of winter and was freezing outside...He turned 2 years old last October.
My cat, Gus, was abandoned. I found him as a kitten sitting in the middle of the road. My boyfriend almost ran him over but saw him just in the nick of time...He'll be 5 soon...He was a pretty young kitten. I think he was old enough to be weaned but he seemed like he didn't know how to eat solid food. He just would shove him face in it and try to suck it up...lol
My cat, Fred (RIP), I found as a stray about a month before I found Eddie. He was about 2 years old and was a very sick kitty when I found him...I lost him last year.
My old dog Dan (RIP) was also a stray. He made his way here when he was a pup of about 5 months or so. He was my boyfriend's dog and when I met my boyfriend and eventually moved in, Dan was already pretty old...some members here probably remember when he passed away...I still miss that old guy terribly...He was about 15 years old when he passed...
There was Charlie, a Cocker, who was probably around 7 or 8 years old. He was VERY aggressive toward people but seemed to really like us. He escaped my yard and was hit by a car.

When he first showed up, he looked like he had been very well cared for, he even looked like he'd just been to the groomers...I'm not sure if he was actually dumped or just lost...I tried to find his owners but no one claimed him.
There was my boyfriend's old cat, Hank. He has been gone for about 6 or 7 years now. My boyfriend found him when he was a kitten, laying in the driveway. Hank was so young, my boyfriend's mother had to bottle feed him.
There have also been many that I tried to get and failed and I remember each of them. It's very depressing to think about.
The cruelty of abandoning an animal is just beyond my understanding. I will never get how someone could throw out another living being like they are a piece of trash and never think about them again. I always wonder if the people that "threw Eddie away" (because that is what they did) ever wonder what became of him. I hope they lay awake at night wondering and I hope that they feel horrible regret. When I saw that innocent little puppy cowering in
fear at my door, I have never felt so angry in my entire life. I still get angry when I think about it for too long...lol Although, I'm very glad that I have Eddie in my life and I know, without a doubt, that he was meant to be my dog, what those people did to him is just...horrible.