Three weeks ago we ended up with a cat in much the same way. Someone dumped it out in the woods and it happened to find me before a coyote or bobcat did. I put it one of the travel kennels in the truck and brought it home intending to give it to our daughter in law. My wife decided she liked it so the cat has remained.
People who dump their unwanted pets irritate the heck out of me. For some reason they believe their pets will magically find a home that will take them in. More often, the pets end up dead in some tragic way. These people are nearly as low as those who abuse animals. The saving grace is the former are generally ignorant while the latter knowingly abuse their animals.
