If they shut down the whole internet, transfers can be made, but not verified. Just like if you use a credit card or check in the modern world. The real question should be, how on earth can they shut down the internet? That would require shutting down every bit of the communications system(and power system), and assuming that all people don't learn how to P2P off an 802.xx grid. Even EMPs would be very limited and at worst, temporary, because you need a lot of power to take down the world's systems.
Want DP delivered to your inbox daily? Subscribe here: