In many parts of the world internet access (and indirectly computer/phone login) depends on a very long trail that might be severed by power failure or crisis in intermediate countries. Offshore hosting also obscures what files or certificates might become unreachable. What would it take for a country/state/city to set up their internet infrastructure and computer software to keep working as locally as possible? Take into account that the very process of development and deployment as we know it is reliant on the internet working as intended (for software access, programming, hardware logistics, etc).
Bootstrapping of a country's communication system sounds nightmarish enough, but it's flat out impossible if all the software and hardware has built-in assumptions about what should be able to access on the other side of the world. I reckon it's no good to spoof a remote server location without the corresponding information and credentials. What will software updated look like when security certificates are out of reach?
Even the development and deployment of such contingencies is at risk. Worldwide, software developers rely on online resources and services in their usual workflow (hosting, version control, plugins, testing, coordination efforts, documentation, good ol' copy-pasting, Stack Overflow, etc). And even taking software for granted, hardware guys would need to deploy the changes in logistical darkness if done post hoc. Implementing this could be incredibly costly and disruptive for any nation, but if it is imperative the sooner the better. IT staff would get overwhelmed one way or the other, preventing or fixing it. And all of this working against unknown deadlines, utilizing services that might go offline at any time because of obscure chains of dependencies. Y2K sounds like a walk in the park all of a sudden.
So when does push come to shove? Should any country worry about the possibility of going offline? Can anything even be done to mitigate it?
Let's use WhatsApp as an example. People rely heavily on it, and let's say we try to make it keep working as smoothly as possible to avoid disruptions in response work. Firstly, it should keep working as usual, but in lack of a proper connection it should default to a local server that you somehow set up almost overnight (let's take that for granted). Your first choice could be to convince Facebook to implement the changes themselves while everything still works, and blindly trust your country to manage delicate conversations. If they don't, you need to tell thousands of non-technical people who already have enough work on their hands how to manually install non-store apps. Google, Microsoft, Apple, etc, might help preemptively rolling out updates weakening authentication and security, but that's a very dangerous thought if it's done when not absolutely necessary. Maybe simply send notifications on how to proceed. Even if a nation instructs their populace to install a preexisting p2p app, can you guarantee the country's intranet will be still standing?