after the great cataclysme all mankind was extinct. all mankind? no, a litte village habitated by brave warriors …
realiter a part of the humanity will surely survive quite comfortly and for a long long time no matter which kind of desastre may happen.
may be on giant rafts, on submarines like capitain nemo, on habitats on the ground of the sea, into deep hollows like the dwarfs, on space stations hundreds of miles over the burned earth or in massive fortresses on the highest summits of the mountains.
the technology today is so advanced, that determinated and capable men could with a minimum of warning prepare themselves for surviving even for generations in an extrem hostile world and saveguard the technological and cultural progresses of mankind.
and you can be assured, those men will be the firsts to know
so don`t be afraid, nothing will be lost.
by the way - have you ever heared the expression" bottleneck effect" ?