So what is this, "Stop Hiding" message. I see posts that say that if you pause while 173 or 106 is near or you are at a death screen, a message appears. So what happens when this message pops up?

It is an easter egg for the menu screen. All it does is close the menu, displaying "STOP HIDING" with one of 173's scare sounds. It usually happens around 106 or 173. It was heavily nerfed a while ago.