Offline signing is common, so theoretically you could print the transactions and private-key to the account/utxo on paper and use them as physical promissory/bearer notes.
Unfortunately though, it's the network that verifies the absence of double spends, so there's no guarantee of uniqueness.
With the no internet, and limited interbank settlement, I would still bet on the value of crypto over the fiat inflation that would be used to facilitate credit-worthiness.
Crypto would only retain its value in such a situation if a significant market system, in real goods, had been developed around it. Meaning you could exchange your crypto for the things you need. (Meaning the seller would have confidence they could do the same.)
It seems like this could work, hypothetically, but given the need we have for the currency of our country, it's hard for me to imagine that crypto would hold its value in the face of some kind of massive computer failure.
Unfortunately though, it's the network that verifies the absence of double spends, so there's no guarantee of uniqueness.
With the no internet, and limited interbank settlement, I would still bet on the value of crypto over the fiat inflation that would be used to facilitate credit-worthiness.