It's not as simple as cash v card. If network connectivity is lost then selling anything becomes tricky because you lose control of the inventory.
I think it depends how long you lose it for in that case. At Coop the stores only fed back stock data to the centre once every 24 hours, last thing at night where 99% of them had closed for the night (there were a very small number of 24 hour petrol station stores that have since been sold to Asda).
Store orders were then generated early hours of the morning which then in turn created the vendor orders for fresh, milk and bread.
Bigger supermarkets might do this more frequently.
But ultimately a store can sell as long as long as it has stock and the means to complete the transaction.
Which asks the question "How did shops manage prior to the internet".
In the 2015 Boxing Day floods Mytholmroyd and Hebden Bridge Coops ended up shoulder deep in floodwater and were closed for a long time. In both cases we ran a pop-up shop from their car park to provide some sort of an offer.
For the first week or so we had power from a generator but no secure data because of the flood damage so we couldn’t take card payments (my memory is vague but I think there’s a requirement for a secure data line for payments so using a mobile phone wasn’t allowed) and couldn’t feed back stock and sales data. So we did it manually and someone in head office keyed the data for us.
But that was a minimal range - about 250 articles compared to say 4,000 for a normal store.
But it did cause the funniest moment of my time at the Coop and at the same time teach me a lesson about different perceptions of the word essential
Hebden Bridge type woman walks up to the pop-up shop in Royd (it looked like a portakabin with a serving hatch)
Her - oh, what’s this then?
Me - best we can do till the flood damage is fixed. We’ve got the essentials though
Her - good, I’ll take a jar of red pesto
Me - ah, we don’t have that. I can try and get some from another store for tomorrow though
Her - don’t worry, green pesto will have to do