This is very important:
The new owners almost always unwittingly encourage the very behavior they don't want.
This is an amazingly difficult concept for most, but it doesn't have to be.
What matters most is that the dog is simply a dog- not an abused dog.
It takes more than love and a good heart. Don't develop a 'loving' attitude of, "Oh, you poor thing," and then coddle the dog. By giving a positive consequence (coddling) to a negative behavior, the owner reinforces the negative behavior. This is what most people do because they feel sorry for the dog.
Now you know what NOT to do. What can you do? Hard to say without knowing more about the dog. Simply put: Reward the behavior you want; ignore what you don't want. This will probably be an oversimplification, but this approach and a good, positive attitude (not a sad one full of pity and remorse over past experiences that are done and gone) will take you a long way.
And make sure the dog gets a clean bill of health. The best trainers in the world can't overcome the effects of a seriously ill dog.