The best case is that a few humans get to live their lives on Mars, the sky above Venus, or under the ice of one of Saturn's moons. Then if Earth suffers a massive asteroid hit or supervolcano eruption there will still be some humans about.
However, it will always be much easier to move lots of people underground or underwater to survive even the worst imaginable disasters. There are probably already a sufficient number of fully stocked underground bunkers to guarantee the survival of the human race from anything short of the Earth spiraling into the Sun.
In any case, we are eventually going to be replaced by genetic mutants, cyborgs, and/or robots. So humanity is doomed regardless.
Don’t be so cynical. I am constantly amazed at what humans can survive. We seem to be the cockroaches of the universe. Have you seen “Touching the Void”? Great book/movie. No food, no water, broken leg (seriously broken, not just fibula fracture) the guy crawled miles at something like 17,000 feet elevation.