Completely isolating the internet within a country is an unrealistic thing to accomplish. It would involve cutting off ALL methods of communications:
- Telephone
- Radio (including hobbyists)
- Television
- Carrier Pigeon
- Flag Semafore
- Probably other communication systems I haven't thought of
But purely as a thought experiment:
As long as there was still an internal intranet and there were enough individuals on that internal intranet running full nodes and mining, bitcoin would still continue to operate. Depending on the amount of hash power that was running on that intranet, it could take hours, days, or even months for transactions to confirm.
Eventually, if the intranet was re-connected to the world wide internet, there would be a massive blockchain reorganization for everyone in the cut off intranet. All of their confirmed transactions would become unconfirmed. All block rewards that any of their miners earned would vanish. Any transaction that included any value from any of those block rewards would become invalid and would vanish. The remaining transactions would have to be re-confirmed on the full network.
In Satoshi's own words back in 2010:
It's hard to imagine the Internet getting segmented airtight. It would have to be a country deliberately and totally cutting itself off from the rest of the world.
Any node with access to both sides would automatically flow the block chain over, such as someone getting around the blockade with a dial-up modem or sat-phone. It would only take one node to do it. Anyone who wants to keep doing business would be motivated.
If the network is segmented and then recombines, any transactions in the shorter fork that were not also in the longer fork are released into the transaction pool again and are eligible to get into future blocks. Their number of confirmations would start over.
If anyone took advantage of the segmentation to double-spend, such that there are different spends of the same money on each side, then the double-spends in the shorter fork lose out and go to 0/unconfirmed and stay that way.
It wouldn't be easy to take advantage of the segmentation to double-spend. If it's impossible to communicate from one side to the other, how are you going to put a spend on each side? If there is a way, then probably someone else is also using it to flow the block chain over.
You would usually know whether you're in the smaller segment. For example, if your country cuts itself off from the rest of the world, the rest of the world is the larger segment. If you're in the smaller segment, you should assume nothing is confirmed.