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.