You just mint Luna at will.

The problem occurs when the amount of Luna that trades for $1 becomes undefined because nobody is willing to do the trade anymore.

Eh, but minting Luna increases the supply of Luna and thus devalues it, therefore a run means that the price of Luna increasingly drops as you mint more, meaning you have to mint more Luna, it heads to zero, you're dead. It's the opposite of stable, because a run actually accelerates itself. What am I missing here?

When the price drops, people on reddit start saying "buy the dip it's going to the moon!" to lure in some new marks.

In the long run you're right though. Eventually you run out of people who believe them and you get the events of the last few days.

You're not missing anything, that is literally how it works and the reason it is now failing.

The balance is ostensibly that you do get some tangible rewards for Luna. But when the expected value of those drops below the outstanding balance as well, you still have a death spiral.

So you’re saying it’s always been a contest of belief.

It very definitely is.

You print luna and 'burn' terra. Or when people get terra you print terra and burn luna. The luna tokens supposedly have value because they get a share of the transaction fees.

The printing of luna when people sell terra should be offset by luna having been burned when the terra was printed. Ideally (when the price of luna is growing) then you print less luna at sale time than you burned earlier when the terra was printed. This decreases supply of luna, making luna worth more.