I suppose your area has houses far apart and so when the dog or cat does wander or is put out to wander aimlessly, it is easy for them to seem lost. I know that in the rural areas, pets are often kept outside and have less than household status on any given day.

That last pup you found surely looks healthy in the pictures. Maybe he/she is just lost? One would hope that the owner would go door to door, looking for the doggie and would eventually the poor thing would be home again. But, if the dog was put out to fend for itself .... no wonder you find so many stays. It seems that they are disposable where you live. You seem to find more dogs than cats. Could that be that cats are oh too often and more easily part of the food chain?

Have you considered opening a 5013c shelter?