Whenever someone brings up the demise of the sun some billions of years in the future as if that has any relevance at all, I laugh. My goodness we can't see a 100 years into the future. The phenomena we re currently experiencing (accelerated evolution) makes meaningless the talk of such lengthy time spans.
However, I will say that if projected technology continues to blossom then I would think dyson swarms will be in our future. There is no reason not to suppose that self replicating machines couldn't build vast habitats by mining material in low G resource rich environments (e.g. moons, asteroids). It is a matter of bootstrapping nano technology, which we can already really see the path to do. Much like the cycle Moore's law increasing in computing capability by continuously using last generation technology to construct the new improved next generation, bootstrapping will take a while but it becomes inevitable that fantastic capabilities lie down the path.
As far as billions of years in the future, I've already come to the conclusion (because of the Fermi paradox), that intelligent species encounter some kind of singularity in their development, that precludes expansion or desire to expand in normal space. Maybe other dimensions become accessible, or species retreat to self constructed virtual universes, or not just the earth is cradle but the universe is merely a womb that will birth higher level "god like" beings (to which we may evolve if we survive), or maybe some higher level intelligence just stops our simulation and we all disappear lol.
If not for the fermi paradox, I would think that we could plant seeds on other worlds, by sending micro craft that bootstrapped life from dna and once again replicating and obtaining local resources. If life is really that extraordinarily rare that we are virtually alone in the universe (I really doubt this), I do think we would have the capability to propagate throughout the known universe.