I think you're imagining mass extinction maybe a little bit too peaceful. People are not just going to stay where they are, complaining that their feet are getting wet.
Wet feet? Are you imagining mass extinction to be caused by rising sea levels? That's a minor problem in the grand scheme of things. Sea levels will take time to rise, there will be adequate warning for the most part. We won't see a meter overnight, more like a meter in a century. Bad, but not that bad that there's no time to react, or even adapt. I mean, we could protect coastal cities with bigger sea walls. Or maybe it's more economical to simply relocate.

I'd be more concerned about failing crops due to unstable temperatures and rainfall. If climate change is a major problem for humans, it will probably manifest itself in the form of a global famine before we see New York go under water.

So those that survive this will be those who can grow their own food... and protect themselves. Which, incidentally, is why I want a gun. Not to protect myself from tyranny, but to improve my chances of survival in the event of the collapse of civilisation. I'd want to be able to hunt, and protect myself and my resources.