You don't have to look far in history to see examples of this. 3rd Reich Germany kept functioning well past the point where it should seemingly have collapsed. Even as the Red Army were shelling Berlin, there were low-level people continuing their work when the sensible thing to do would surely have been to get their family and flee.

More recently, the Greek financial crisis put a major strain on institutions that were weak to begin with, but there was no rioting or major breakdown of order.

I think modern, Western societies are surprisingly resistant to a breakdown in order, simply because most people have never experienced anything other than order. As a result, acting in an anarchic, non-system way simply isn't something that would occur to them. Even in the face of an existential crisis, they would "keep calm and carry on", because they can't imagine doing anything else.

I think if there's going to be any place that a bit of society is left existing after apocalypse will be somewhere in the US, perhaps much closer to where those billionaires reside than they think (so there's no need to run to New Zealand).

I think the better investment would be to literally convert some of your 'paper' wealth to physical means of production of basic goods.