That scenario is very unlikely, but assuming it happens there will most likely be people, businesses, nodes, wallets, internet cafe, etc that manage to stay online maybe via satellite or other special means. They stay connected globally while private local devices connect to them, mostly to access their wallets.

If international or global internet does not exist atall at that period, permissionless intranet or local/national Bitcoin networks of nodes and others would form around the world. But the most trustworthy and reliable networks from one or few places would be connected to by people from other countries via SMS, radio link, etc. I think reliable Bitcoin companies or organizations will be responsible for facilitating secure transactions between them and the individuals from other countries.