I was a little unclear on your post. Are you worried about the cost of buying a dog or the cost of maintaining them? If it's buying a dog, why not ask around family and friends if anyone has a litter of puppies they are giving away (unless you want an older dog). There are also animal shelters that you can try. There will be a fee (usually around $50). Another place you can try is the classified ads of your local newspaper. Many times there are people giving away dogs.
I always think of elderly folks who become ill or simple can handle the daily routine of taking care of a dog anymore. I don't know if there is a network for this type of thing.
You could also try your local veterinary clinic. I know when I take my dog in for her appointments, the bulletin board is filled with signs from people giving away free dogs and cats. This is usually the first place in the community that people post these types of things because they know other animal lovers will be there.
I hope I haven't misunderstood your dilemma. Please let me know if I have.