I think that at least some people (and when you're dealing with galactic timescales and spaces, this means a lot of people) would stay in reality to figure out how to get around entropy and heat-death.
So even though we might very well be in a simulation of VR-checked-out civilizations (or even if we aren't), I would expect to see some people in our simulation/reality fighting against the parameters of the simulation/reality that puts a time-limit on existence.
It also follows: If it is possible that one civilisation spreads itself in this manner, it is likely that we are decedents of that civilisation. Simply because there will be many more copies of the original civilisation with a penchant for spraying their seed around than other kinds of civilisation.
An _actual_ replicating Von Neumann probe, that we can imagine working within the laws of physics today (even if we don't yet have the engineering capacity to build) can actually clone not just a couple of DNA strands, but can bootstrap an entire new sapient civilization, including technological progress, likely all the way down to the civ's culture.
Most civilisations will have just enough of a life support to keep the machines running. They might be spurred into action each time a sun burns out, but other than that why bother with the outside world?