[8organicbits]

When the network is segmented multiple chains could form. Likely KZ would have a very low hash rate, so that segment would take very long to form blocks (or never complete any). Once the networks rejoin, the global chain almost certainly "wins" and the local chain is ignored. Transactions written to a KZ block will show some confirmations, but won't remain in the eventual dominant chain.

[nybble41]

The global chain will "win" but transactions made in the local chain can be retried in the global chain after the networks rejoin so long as there are no conflicts. Absent deliberate or accidental double-spending, the biggest source of conflicts would be the mining rewards from the local chain since these rewards never existed in the global chain and cannot be carried over. There is a 100-block waiting period before mining rewards can be spent specifically to avoid this issue for shorter-term forks, but it could still be a problem in the event of sustained network fragmentation.

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.

[0] https://blockstream.com/satellite/