It also happens when you have stuff to sell, but the folks who would normally buy it from you can't pay you enough to survive today, because they don't have anything to sell,

It seems unlikely that you would have a skillset which allows you to produce valuable stuff only for poor people, but you wouldn't be able to produce valuable stuff for anyone else.

Okay, thinking hard, I can make up some situations like that, for example that you are a skiled translator into some kind of indigenous language, where all speakers of the language are too poor to actually pay you for the translations (even if they would like reading them a lot). Or that your services are limited to your local area, e.g. you can provide accommodation for people, but there are only poor people living in that area, and zero tourists.

and the problem can start randomly and build on itself

Something like... million people living on an island, where most of them can provide some valuable service to their neighbors (but not to anyone outside the island), but some critical skill is missing on the whole island... like, all of them are genius teachers or movie producers, but none of them can grow food... so they are all going to starve, despite being so skilled that an average inhabitant of the island would be a rich person if they would be teleported into our society?

In short term, this certainly can happen, especially if the situation can change overnight. Like, yesterday, there were hundred specialized food producers, but by miracle, all of them were killed by a lightning during the night. To make it sound more likely, all of them were at the same place (the annual food-producer conference), and something exploded there and killed them all.

But... I don't see how any other economical system would deal with the fact that, no matter how you distribute the money, there is not going to be any food in the island anyway. With free market, at least now all professors and movie producers see the opportunity to become millionaires overnight if they succeed to reinvent e.g. the lost art of picking fruit. Even if they would be great movie producers, but quite lousy fruit pickers.

(Actually, such situation would be made worse by an unfree market, for example if the government of the island would insist that the wannabe professor-becoming-fruit-picker is legally not allowed to pick fruit because he doesn't have a diploma from Fruit Picking University; and any attempt to illegally do the job he is not qualified for would get him arrested.)

Now, let's assume that the island actually is okay, able to grow its own food, etc. It's just that the money flow happens to be hopelessly unidirectional. No one outside the island wants to buy anything from the island. (Let's suppose they are not interested in your stuff, and you can't gain customers even for trying to sell really cheaply, because the costs of ship fuel will still make everything more expensive than anyone is willing to pay for.) On the other hand, people on the island sometimes buy something from the outside, e.g. because they cannot produce their own iPhones. Thus, money only ever goes out of the island, but never in. The island is constantly losing its global PageRank, ahem, money reserve. What happens now?

If I understand it correctly, the standard market outcome will be that -- assuming the island uses its own currency -- the exchange rate will gradually approach "1 out-of-island currency = infinity island currency". The people on the island will stop being able to buy stuff from outside, because it will become astronomically expensive for them.

Yet, within the island, people will be able to sell to each other, because both sides will pay using island currency. And there will be things to sell, for example the locally grown food. No one will be able to buy iPhones anymore, and that sucks, but the island will still be not worse than if the rest of the world would simply stop existing.

And if someone comes from the outside, and uses their infinitely valuable out-of-island money to buy the local food, then the assumption of unidirectional flow of money is no longer true; we now have money flow in both directions.

Etc, economics 101.

However, one possible solution for "people who have nothing to sell" is generally known as Basic Income. Not universally accepted, of course, but it is a way to make sure everyone can buy stuff, at the cost of doing relatively small damage to the economy. By relatively small I mean, of course entrepreneurs will complain about higher tax rate, but as far as I know, they usually complain much more about regulation, bureaucracy, or unpredictability; and Basic Income doesn't create a lot of these compared with the usual government interventions.

Essentially, Basic Income + market profit seems like a plausible approximation of our model of terminal + instrumental value, when we assign approximately the same terminal value to each human (expressed as Basic Income), and more instrumental value to people doing useful stuff to others (express as the market profit).