They are, kind of, not really uncollateralised, but the collateralisation is ugly and not very good and I guess “algorithmic” sounds better. I’ll try to explain.

Algorithmic “stable”coins like this generally work by issuing two coins: one pegged asset that’s meant to be worth $1 (UST) and one floating asset that’s free to have a price set by the market (LUNA).

Your job as a “stable”coin algorithm is to keep the price at the peg (1 UST == $1) even when an imbalance of supply and demand pushes it above, or more likely, below that price, just by issuing and doing things with those 2 coins. On the plus side you can issue as many as you like.

Assuming a liquid market (an AMM like Uniswap will do), you can always reduce the price of the pegged coin (UST) if it goes above the target by making and selling enough of them [1]. (This part is easy.)

When the price goes below the peg, though, you need to create enough buying demand for the pegged asset (UST) at $1 (or whatever) to take all the sellers offering a discount out of the market.

If you did a good job creating value (or at least a non-zero market price) for your floating asset (LUNA), perhaps by building a payments network on its underlying blockchain or pitching really well to a bunch of VCs (maybe both!), then a way to do this is to issue more LUNA and use them to buy UST.

The problem is that just issuing more coins obviously does not create any additional value. It sometimes looks like it does, because markets aren’t perfectly rational or instant, or because of an expectation that the money raised issuing the tokens (/money/equity/bonds, whatever) will be spent wisely to create value. But if all else remains the same, doubling the number of the floating asset (LUNA) will halve the price.

Put simply: issuing more tokens like this is not creating value, it is transferring it from existing holders to whoever holds the new tokens (often called “dilution”).

The first observation here is that in the limit, if I print an infinite number of my floating coins and do nothing else, the most value I can get is the total value of all of them (their “market cap” [2]) before I started printing.

The second observation is that if I’m able, on average, to increase the (perceived by the market) total value of the floating coins (LUNA) faster than I dilute their holders by issuing more (even if it’s just a rising tide lifting all boats), the price should go up and everything might just look like it works.

But if the issuance needed to keep the peg is consistently above that growth rate (LUNA is diluted faster than it creates value), the price will go down. If this happens for long enough and nobody expects it to stop, people will start to sell, pushing the price down more. The lower the price, the more issuance is needed to do the same amount of stabilisation, and the more that will impact the price, etc. (This is the death spiral.)

So I’d argue that UST was (is?) in fact collateralised by whatever fraction of the total network value (market cap) of LUNA can be successfully taken from its holders without initiating a death spiral. This was (clearly) not nearly enough. In fact, given the more volatile nature of a floating asset that’s at risk of dilution and is valued more like a startup than a treasury bill, one might wonder why anyone ever thought they could keep an algorithmic stablecoin stable indefinitely…

Note: when things were looking better the LFG also bought a bunch of assets (bitcoin) as a kind of emergency fund. When everything started to go wrong they also used this in addition to newly minted LUNA to try to support the UST price (by buying it) but this was still just using value from the Terra ecosystem to support the price of UST. They did try to build reserves in good times to support in a crisis, which is sensible, but if doing that still doesn’t prevent you diluting faster than you create value you’re still going to be in trouble.

[1] Generally it makes sense (as far as any of this makes sense) to sell them for the non-pegged asset (LUNA) to push its price up, and to burn (destroy/remove from circulation) them if possible, which might push the price up a bit more (but probably shouldn’t, if you can issue infinite of them anyway).

[2] This is in reality more complex than just market cap, but it’s close enough to be illustrative of the fact that the market values the whole pie (network/protocol/company) at some amount, and that amount doesn’t change no matter how you re-slice it.