This is not that hard. Each store can keep a local record of what is going on. Back in the "dark ages" this was done anyway, credit card transactions were settled at the end of the day. Inventory at a physical location can be tracked locally and updates sent to a central system later to figure out what needs to be restocked where.
Unlike other distributed databases you don't have one store selling an item of food from another store (especially if your online system is down) and need to do a split brain recomp.
Enough people rely on debit cards nowadays that only work online that it would still cause significant disruption. Enough that it's probably not worth keeping the stores open until it can be fixed.
I don't even know a single person with a credit card here. Everything is done with debit cards which require being online to check the balance and reject the transaction if it's insufficient.
In sweden they don't - at least not on the debit cards, which are common. They also just removed the holder's signature field too, nobody ever uses that (it's authenticated with pin + optional ID).
There are a couple of approaches that could involve multiple payment providers over redundant networks so switch to something else.
For inventory, since it’s likely only temporary transactions can be stored locally and then synced when back online.
Theoretically the design could be distributed all the time and just keep working the same while disconnected with some potential reorders and restocks slowed down or delayed.
They'd have to make that very clear at the entrance to the store. This is just a guess, but I think most Swedes don't carry enough cash to even pay for groceries when they go shopping. I haven't had any paper money in years, just a few coins.
But if the store in question would accept cash, then it could at least server some of its customers. I expect it would not only be 15% of the customers. I would add those customers who are, you know, a little capable of adapting to circumstances and would actually go to their ATM to pick up some cash if they don't have any in their wallet. If not, I guess they don't need those groceries so urgently.
I think you're underestimating how little we use cash. There aren't even ATMs in some parts of town and there are plenty of villages without one for tens of miles. Nobody uses cash anymore. It's all either debit cards or direct transfers (either via and app or the bank.)
Treat it as "card not present". Write down the card number, expiration, cvv, name, and zip or equivalent. Get a signature and process it later. If you can't process it later, your system design is flawed.
Unlike other distributed databases you don't have one store selling an item of food from another store (especially if your online system is down) and need to do a split brain recomp.