In the scenario of planetary extinction, it does not seem out of humanity's technological capability to build an ark to seed life on other (extrasolar) worlds. Granted, of course, that no higher life forms will survive.
Several micro-organisms are hardy enough to tolerate the harshness of space conditions, such as severe radiation and the lack of water or oxygen. They may not thrive, but for the purposes of an ark survival is enough.
I imagine a large vessel filled with several chambers, or pods, each vacuum sealed. No additional protections are granted to it, save the hull of the vessel, which provides some measure of radiative shielding. This vessel is targeted at a particular system, being propelled at very low sub-light speeds. It is slow, but it is expected to survive it.
Several redundant computers, each set to wake at infrequent intervals, maintain the minimal systems on the vessel. There is little to do for the journey, since there are little to none life support systems, and the ship is not actively propelled.
On arrival, simple planetary analysis procedures are used to study the planets in the system. Then, the target site and lifeform combinations most likely to sustain life are chosen, and the appropriate pods launched to seed the site with life.