If it’s nuclear war then that mass of people will be dead, injured, or sick from fallout.
If it’s an asteroid strike then they will be dead and injured. (But no radiation)
If it is an EMP then the vault dwellers will need to be far enough from any cities that they will ) remain undiscovered for as long as it takes for the mass of people to starve to death. About two or three weeks I figure.
Listening to this book ( read it once before) about an asteroid strike. It’s a very enjoyable story, written in the 70’s.
https://www.youtube.com/watch?v=Zp9xFO2xS6Q
2 or 3 weeks to starve to death??? That will be about the time the masses will start getting lively and creative looking for grub!
My grandfather made it 3.5 years on for the most part a handful of rice a day...