Would they bump into each other at the mall?
The only thing in the historical record which "might" reach that level of extinction in a short term event would be a asteroid strike.
All out nuclear war doesn't even come close.
The obvious thing for survivors to do would be set up a radio station and advertise for other survivors to come to them. Survivors would probably be clustered around each other.
All survivors would have abundant resources. Other people would be highly valued.
It would be a golden age for a few hundred years, until the population bred up enough to develop separate tribes and nations.