They are now disconnected from the global Internet. What happens to all BTC transactions made in Kazakhstan? Will the local network accept them? What will happen to them when the Internet connection to the global world is back?
On the bright side, it's not necessary to have full Internet connectivity to keep the local chain in sync with the global chain. A single local node with access to the global blockchain (via a VPN or dedicated satellite receiver[0] or multiple upstream Internet connections near the border) can ensure that the local chain is constantly synchronized with the global one, and even forward local transactions for inclusion in the global blockchain.