James Howard Kunstler, who writes about ecology, global warming, peak oil, and so on, wrote a quartet of novels under the heading "A World Made by Hand". Kunstler's story is post-collapse, post apocalyptic. He doesn't dwell on the event that finally collapsed society, but here we are in a small, up-state New York town, representative of where the world is at. No oil, no electricity, no internet, no telephone, etc. etc.
People are required to live (at best) at a 19th century level (not that bad, really) except they don't just naturally know how to do that. They have to figure it out. There is of course a huge population loss. Even though the people in the novels understand what causes disease, they don't have the means to deal with infection, for instance.
Despite all that, the novels are fairly up-beat. In the end, enough people survive well enough that they can have hope -- provided they are very disciplined, and maintain the steep learning curve of 19th century survival skills. (In some ways, "19th Century" has to refer to the first quarter -- not the last quarter of that century. In other ways, people will be forced back into the 17th century -- simpler technology. Unfortunately (and this is the message of another very good novel,
Earth Abides) succeeding generations will know less and less about the 20th/21st century ways and means. The most pessimistic approach to this problem is
A Canticle for Leibowitz which is set in a desert monastery after nuclear war. Society, such as it is, has been pushed back to the medieval period. It takes roughly 2000 years to fully recover, at which point they have another nuclear war. Great novel.
For instance, one can make soap out of used fat and a caustic extract of wood ashes -- but one has to know how to do it (otherwise one just ends up with gritty grease, not soap). One can preserve meat without freezing, but one has to know how, exactly, to do that -- otherwise, one will die of food poisoning (botulism, for instance). It's not hard to preserve cabbage as sauerkraut, but if not done correctly one ends up with a stinking mess--the sort of thing one finds in the distant reaches of one's refrigerator every now and then.
Will humanity die out? No, I don't think so -- but a lot of people might wish they had died sooner, once social collapse gets under way.