Once the very last remnants of the very last stars have finally decayed away to nothing, and everything reaches the same temperature, the story of the universe finally comes to an end. For the first time in its life, the universe will be permanent and unchanging. Entropy finally stops increasing because the cosmos cannot get any more disordered.

Nothing happens and it keeps not happening. Forever.
Physicist Brian Cox, on the heat death of the universe. From The Wonders of the Universe: The Cosmos Made Conscious