There are projects like Phonon from GridPlus which use industry standard hardware to enable secure, private, offline trading of units of crypto. This is effectively digital cash. https://docs.phonon.org/readme
They either stop working or they're vulnerable to a double spend attack. Until the servers come back and processing payments continues, there's no way to know if your customer has already spent the crypto they're supposedly transferring to you or not. Double spend attacks have been used in some scams already where the payment system didn't wait for the payment to make it to what becomes the "right" chain (validation takes up to 1½ hours with Bitcoin, depending on how many blocks the payment provider waits before assuming the transaction succeeded).
You don't need to take down the entire internet to sabotage cryptocurrency either. Many cryptocurrencies rely on a few key validation servers as running and processing the entire block chain all the time becomes very resource intensive as crypto gains popularity. A strategic attack on only a relatively small amount of servers (8000 in the case of ethereum and all coins using that blockchain) can DoS many cryptocurrencies worldwide. Furthermore, over 46% of Ethereum's servers are controlled by two parties, so if a government can seize those companies it's likely capable of doing a 51% attack to sabotage many cryptocurrencies used on exchanges today.
I doubt there's any risk of sabotage in practice, but like most digital payment methods, this stuff only works if there's an internet connection.
