What happens that far in the future is non of our concern, nevertheless less. According to Stephen Hawking, in a recent seminar, mankind has to find habitable earth like planets to which it can escape from the coming cataclysm. This will not to do with
the demise of the solar system billions of years hence, but the certain ecological destruction of the earth due to population increase. There is no doubt he says, we have only 10,000 years to leave.
A1 development is certain to end in failure , he adds, because human development will be dwarfed by artificial intelligence built with self replicating and self developmental capacities, making humanity redundant.
With these short term projections, the fate of our solar system will not be our concern. We may never know it's fate, since we will not be here, if we survive AI and can escape the barren earth left devoid of its rescourses, we will wake up in other worlds, not really knowing our origins on planet earth.
In fact we may look at the solar system, from afar, not really cogniscant of whether it is still there, or are they merely the remaining light emitted from them a long time ago, the length of which would be changed relative to the aberration of time-space.