As far as I know, an 'invisable fence' is a wire that is usually buried on your boundary. Your dog wears a collar and when it tries to cross the boundary, it gets an electric shock. So basically, an electric shock collar to stop your pet escaping, but requiring no supervision like a 'normal' e-collar.

To the OP. In your position I would consider supervision when you ar ethere, and keeping the dog indoors when you are out. It is not safe for your dog to leave him in the garden alone when you are not at home.