You can do offline verification of payment cards, there's just higher fees and lower limits on payments.

This is a common way people get their current accounts into debt without authorising an overdraught.

When I was a kid, I remember the cashier at a department store checking a book for my mother’s credit card number.

I misunderstood the nature of the book, assuming it was a list of valid card numbers. It was, of course, the opposite, so when I said to my mom “I hope they find your number in there” she replied “I hope they don’t!”

It's used by alot of vending machines or public transport. The bus can be off-grid while still allowing a ticket purchase.

Im not that familiar with the protocol, but i could see there being a special clause to allow larger off-grid payments in emergency situations.