The people left will work, there's just going to be a lot fewer people. Just as the horse population dropped drastically since they were no longer needed to make the economy go, so to will the human population. And why not? The best solution to human-climate change is fewer humans. It's not like there going to force you to not have kids, it will just feel like having a family is too hard, and more and more people will put it off, and we'll be ok