I'm sorry for the situation your'e in but cannot understand why, if this lady is capable of taking her dog to the the vet on her own, cannot clean up after, see is having(or not having sufficient water/food for their needs) and care for it in her own home. I know you have been cleaning up the dog and floor but how is it that she has not seen what's going on. I'm not having a go at you in any way at all, you obviously care very much and are helpless in a lot of ways regarding what's happening. Do you know if the dog came from a rescue centre at all, because they often have a policy that the dog 'is only adopted and always belongs to the rescue, n they should be informed if someone can no longer look after them'. If not then is different situation n don't think a dog can be/taken by authorites(rspcsa etc.) euthanised without the owners consent unless deemed otherwise. Whatever happens i hope the dog, if suffering so much and no chance of recovery, you and the owner can find the best way soon. I walk a dog for an elderly person n know they mean the world to each other so understand in a way although can't really know what's going on with what you're dealing with.
Hope things work out for the the best, stay strong
H.