the other dog died in the hospital, this has happened once before, but on our property and she was restrained properly. During the attack my dog's collar came off in all the lashing, the fight was broken up by a neighbor with a hard object. Tennessee state law dictates it must occur on the dead dog owner's property, and it did not, but the fact it's happened before worries me and the collar coming off could be classified as neglect. Also the owner declared she did not know her dog was loose.
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If your town has a leash law (and most do) and your dog was not on leash, then it will likely be viewed as both parties' fault. The fact that your dog's collar came off during the fight might be negligence but it is not "neglect". The fact that the other owner didn't know her dog was loose is irrelevant. I wouldn't worry about the other incident unless your dog was deemed "dangerous" and it does not sound as if she was.
I assume animal control or the police were notified and I don't know what the other owner is asking for, so it's hard to say what you would be liable for. In most instances liability would be the vet expenses relating to the fight and the replacement value of the dog.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.