If an earthquake hits an area, and facilities used in accessing internet connection destroys, internet connection maybe paralized and it will be impossible to access the internet. We can't do anything about it but to wait until everything is fixed and normalized.
If internet continues nothing will happen to cryptocurrency. It will still hold the market and people will recover their deficits without affecting crypto market. There are many big natural disasters in the world but we observed that dollar didnt affect. The reason is that it is mandatory for survival. The same thing will happen in future disasters.