I recall many people using a similar phrase, but no one would use the word "slave." They would call them "the society."
I can remember one time, when my mother disagreed with how an elder had interpreted a letter from the GB to the congregation. She said that she would "wait for the society to clarify the matter." When I asked her what she would do if they did not provide this clarification, she simply repeated that she would wait for the society to clarify it.
It was an interesting experience. She was (and is) a die-hard hardcore JW. To her, the society (ie, the GB) is the first and final word on any issue. So she was going to wait for them to provide a clear understanding of whatever the matter was. But by doing so, she was also ignoring the advice of the GB to follow the guidance of the elders. I didn't press the issue, as she seemed a bit distraught and she doesn't handle cognitive dissonance very well. But it was an example of the kind of mindset that is created by their policies and doctrines.