collapse of the old society

there will be ridiculous civil unrest, incomprehensible numbers will die

If things get desperate enough direct conflict between nuclear powers of basic resources like food and water could be a thing as well. Sure, life will survive. Microbes for sure. Abyssal creatures probably won't notice too much of a difference if they aren't oxygen starved before then (not sure about how much of a risk that is)? Some species or plants and animals are hardy enough to survive and some will get lucky.