I do not know how will it happen as it is equivalent to saying what if networks stopped working and internet gone. Let's us assume your fantasy even it happens then for short period of time u will see some rage moment across the globe and it might lead to big chaos scenario and we might see major accidents.
Cryptocurrency can still vanish without shutting down the internet. It could happen once the government order its citizen to stop using cryptocurrency for certain reasons. Even though most of the cryptocurrencies are decentralized, they can't still stand against the government because it is still mandatory to follow its orders or else you will end up in jail.
If the government really had the capacity to control and manage crypto, crypto were not able to grow until now, you can see a lot of bans have been issued and then repealed, all of which is useless with crypto, that means crypto will not disappear unless the internet is completely destroyed. But the internet is always a very important and secured network, if it is destroyed, not only will crypto disappear, so many other products will disappear similarly, I do not believe that the authorities may be careless in this situation
Authorities have a capacity of at least partially control and manage crypto by the law, which is already imposing on companies verification of the users (including checking your source of income in some cases) and managing anti money laundering. As well in some countries, you cannot buy legally some cryptos using fiat (unless it is otc cash transaction with individuals).
But in many cases approach "why to ban it if you can tax it" is starting to prevail.