Worrying about Earth's destruction a billion years in the future is somewhat quizzical whether the question is still open whether Mankind will survive it's own childhood. Let Human civilisation survive it's first 100,000 years first. If we make that benchmark, then we can worry about the Far Far Future.
LazarX,Not worrying about it is already being done.New stellar science shows that stars do not follow the natural timing sequence currently modelled, and new projections that include non-sequenced failures in stars is being developed.A recent article here has a link to that story.I agree that we must survive our own childhood first, otherwise we would be taking the human disease into space. Only mature species should do real space travel, thereby perpetuating their existence beyond their star's life cycle.