What would happen if a country was suddenly vacant?

It’s dangerous to assume that a trend will continue indefinitely. Most likely the trend would be modified before it got to that extreme. From Mark Twain:

This thread shows the importance of every country having a government in exile.
The US has such a strong ex-pat community that forming a government in exile is
a real option.

But in any case, a government in exile can take the UN seat of the “disappeared government” and we can move forward from there.