The Earth is the only habitable place in the solar system. Everywhere else requires humans to bring along their own life support systems, fresh water, and means

The Earth is the only habitable place in the solar system. Everywhere else requires humans to bring along their own life support systems, fresh water, and means to produce food. Human occupation of any body in the solar system or artificial bodies like a space station will always be limited by the amount of high tech infrastructure that can be built there. Even on Mars there's no guarantee there's enough in situ resources for humans to be self-sufficient. So the only was an extinction event on Earth would be survived by off-world colonies is if they were 100% self sufficient. Even a broken toilet could kill everyone in a space vehicle, human lungs don't appreciate aerosolized shit in them. Building a permanent off-world base is a huge undertaking. Building an actual colony is an order of magnitude more difficult. And building a completely self sufficient colony is several orders of magnitude more difficult than that. In any sort of near term setting an extinction level event on Earth is going to lead to the extinction of all off-world colonies/bases. They stand even chances of completely dying out even with unlimited support from an intact Earth. A solar flare could wipe out a space station or Mars base. A GRB capable of wiping out life on Earth will wipe out life pretty much everywhere in the solar system.