This is taking a very hypothetical situation, as I know the Internet is no easy thing to bring down. While it is a great thing to have an exchange of value without needing the government or a central bank, the downside is.. what happens in the situation where the Internet is knocked down? As we move further in to the future, it seems a good portion of everyone's money will be in cryptocurrencies.
You cannot hold a piece of cryptocurrency in your hand, all they are are lines of code.
Lets say in the future mankind is 100% in digital transactions with cryptocurrencies. If the system goes down, lets say a worldwide hacking, it would evaporate any proof of what you own online and any means of transaction as well.
It's a moot point, if all the computers died the entire economy would collapse since much of the financial industry is held on fractional US dollars.
At the end of the day we would go back to a barter system, if you wanted something like food you would trade something of value, like ammunition, gas, or something else.
Everytime I see this question asked online I just laugh. If an EMP went off across the globe there would be much more severe issues than, "What happened to my cryptos?". Anything with a circuitboard would no longer work. Even the tech that would still function afterwards would be inhibited greatly due to the fact that the infrastructure supporting just about everything that we use on a daily basis is completely destroyed. The real question here would be how drastically would this impact human life? How many people would end up dying because we cannot support the amount of human life on this planet without the assistance of computers? How long would it take humanity to recover? Your cryptos would be unrecoverable and gone forever, but you couldn't even use it if you could recover your coins since an EMP would destroy everything that you could use your cryptos with.
Perfectly!