We as civilization are not willing to prevent that event, nor able to fix/repair what it will do, so what makes you think that we might be able to do anything with faster events like a supervolcano eruption or a big enough asteroid impact?
off the top of my head, given unlimited budget, I'd probably have a massive vault of seeds (not just in variety, in quantity, too,) and adequate staff in rotations in a deep-sea bunker. not near a fault line, but deep enough that surface conditions are less likely to impact (no pun intended). Sea vs land because "digging your way out" become less of a problem. If you had a truly unlimited budget, one could imagine an Ark of embryos and a sufficient population of young does of each animal species you sought to preserve.