I was wondering if you have had any experience in helping abused  animals and law enforcement? The reason I ask is I am trying to help an  abused dog.
Last month our next door neighbors had a woman move in with them.  She brought a dog. They put the dog in a cage ( 4 by 4 feet) with a tarp  over the top. The cage has a wood floor. There is nothing else in the  cage. No toys, chews, hay, dog house..nothing. They give the dog food  and water in the morning and that is it. They never speak to the dog,  pet it or pay any attention to it.The cage floor was kept clean.  I did nothing at first because i was not sure if this was a  temporary situation and perhaps the woman was down on her luck and was  maybe looking for a place for her and her animals. Anyway about a week  ago I began to notice the woman was no longer around. The floor of the  cage began to pile up with feces. I went over to our neighbors and asked  about the dog. The owner of the property said that woman had to leave  for a few days and he said he does not really like the dog and he is  scared of it. So I offered to walk the dog and look after it but the man  said he will have to ask her first....Anyway two nights ago there was a big rain storm with lightening  and thunder. So again I went over and asked the owner of the home if I  could put the dog in an enclosed shelter for the night: out of the rain.  I told him we have an enclosed shelter.  He agreed and we took the dog into our home. He was so thirsty and  hungry, he drank five bowls of water and ate three full cans of  wellness. Now I have been checking on him and I see they give him food  so I am not sure why he was so hungry. Here is the other strange thing.  From looking at him through our window it is hard to see him clearly but  once we had him in the house it was clear he is extremely under weight.  You can see his spine and ribs easily. I picked him up and he did not  weigh more then 20 or 30 pounds...He also is kind of  wobbly on his feet, (like a man that has one drink to many). One side  of his face is pulled up higher than the other side. He has a cyst on  his chest that when touched is painful to him. I could see him wince. he  also has hot spots on his feet...The next morning the woman who owns the dog came by to get him from  me. I tried to keep it lite and i told her how nice and smart the dog  is. She gave me a phony story about how she was in a car accident and  that is why she was not around, she even added a tear in her eye to show  how concerned she was. She told me she has owned him since he was three  and he is twelve now. She then said in a song song voice " mommy is  taking you home now". Apparently home is back to that cage because that  is where he is now.
I found a rescue group that is dedicated to helping chained and  penned dogs and there is a person that I am in contact with. They are  helping by listening to me and offering advice. 
In fact the woman that started this group was arrested once for  taking a dog off a property. The dog had been laying on it's side for  three days in a yard and could not get up...So she had no choice but to take  the dog and bring it to a vet. So she was arrested for stealing the dog.  Long story short she refused to give the dogs location and the dog  lived in a secret home. The prosecutor and AC refused to look at the  photos and video of the dog in the yard. It is a well documented story  with news paper articles to back it up. It all seems very grim and  stupid.
Here is my plan. I am going to tell the woman that I have been  looking for a nice friendly pit bull like her dog for a while now and I  will offer to buy it. I don't want to go on about how much better i will  treat it because I don't want her to be defensive. I will just keep it  short and sweet. If she wants more info then I will explain that I plan  to keep it as part of the family and take care of it etc....
I have already called animal control ( our animal control officers  seem to be very concerned about animals unlike the other stories I have  read ) and checked with them. Terry and Debbie ( we have two AC's) said that the dog must have a  shelter not a pen by law and also if he needs medical care the owner  will have to provide it. I explained my plan about offering to buy the  dog and they think it is a good idea. They are on standby and are  waiting for my follow up.  If the woman does not want to sell the dog then I will make a  complaint with AC and ask them to investigate. I will then keep in touch  and follow up. If the woman does not want to help her dog I am hoping  the pressure from AC will either help the dog or cause the woman to sell  it to me.
Is there any advice or experience you might have? I am willing to help this dog in whatever way I can.
Don, these are always difficult situations, and honestly it sounds like you're doing the right thing.  You do have to be careful in situations like this, as legally the lady owns this dog and if you take him, even for good reasons, it's no different than you taking her TV or couch.  However, there are laws against both abuse and neglect.  Abuse is usually more straightforward as there are wounds and signs of being physically beaten.  However, neglect can be just as bad or worse, and is also just as illegal.  You can't in good conscience ignore either situation.
In this case it sounds like it's neglect, and based on what you've described it's probably criminaly prosecutable.  First I'd say try to get photos and videos of his normal environment.  This will help support the case if it ever ends up going to trial.  You've already done the next step of contacting your local animal control division, and thankfully it sounds like you have some good people there.  Most animal control officers really do care about the pets they investigate, but this is also one of the most under-funded departments and they usually don't have the resources to fully investigate every case like they wish they could.  But in order for anything to be legally done, the officers have to be the ones involved as you can't bring a criminal case against someone without being in law enforcement.
I really admire how you've decided to handle the situation.  Offering to take the dog sounds like a great solution and if it works would likely take care of everything.  However, I have a feeling that she won't be willing to give him up, which will complicate things.  I can't give better advice than what you're doing, and think you should proceeded as you've laid it out here.  You seem to have things well under control.  
But please let me know how things turn out!