The concept of invisible dog is quite the opposite of what a dog stands for literally. Dogs are not animals that are given to being invisible. Most have dogs as a pet, some for security reasons. All the same, dogs can sneak up on you sometimes though, and you would wonder where they came from.
I am trying to pinpoint an angle with this invisible dog thing, but it is expressionless. I saw something online about how an invisible dog is used to describe security details, fences, and maybe cages. That's not really a good description though but dogs can be all over the place.