All forms of energy ultimately end up as heat, and the point at which all temperatures at all points are equal is the point at which maximum entropy has been reached and the universe is "dead" (see: Heat Death of the Universe)
Actually, heat death of the universe may not be an issue but rather death of the local region would be the issue.
Since the expansion of the universe continues to accelerate, in the time scale of trillion-trillion years, the nearest galaxy (or even the nearest star) will be "receding" faster than the speed of light. The nearest star is not "moving away" faster than light, but the space between us and it expanded. When the added distance due to expansion
dX/dT > c they are receding faster than the speed of light.
Once the dX/dT > c is reached, it is "receding" so fast the light it emits cannot get to us. So, when all the visible light or available energy within our region are gone, our "local universe" is dead.
In many ways, we are lucky to live in this time frame. We have enough visible systems that we can deduce the original of the universe: big bang. It happened not so long ago that we can tests the big-bang theory by detecting the left over microwave.
When most systems already receding faster than light, living beings then would not see super clusters galaxies. Some point later, they will not see super clusters but only the local cluster. Some point later, they will see only their own galaxy, then only their own local star cluster, then only their local star.
At that point in time, they don't see enough to deduce how the universe started. The background microwave would long since disappear. Trillion-trillion years from now, folks will not know there are more stars out there. No dust cloud, and nothing to deduce how their sun was formed.