This is an example of an experiment that can be easily proposed, but never carried out in the real world. To test what happens to time in this way, you have to stop the universe from expanding, and eliminate all relative motion. This cannot be done. My guess at the outcome of this experiment is that without motion of any kind, time becomes a meaningless 'dimension' by which to interpret the world. We know, however, that at the level of the quantum world, there is no such thing as a 'static' timeless system. All things are ultimately being jostled about by what are called quantum fluctuations of the vacuum state. And what these have to do with, no one really knows.