At a centralised extreme, where there is only one issuer issuing the IOUs, stability can be attempted by the simple stategy of "buy low, sell high" on the part of the issuer-as-marketmaker.
Take for example bitcoin, being as how it was the first example of a cryptocurrency.
(There is a "twist" coming in doing that, but hopefully doing it will illuminate the "twist" itself also.)
Suppose the issuer, which is to say (to use set theory terminology) the set of all miners, had simply made sure to always and without fail operate as market-makers, using a "buy low, sell high" strategy.
Every iota of negotiable value any miner managed to "sell" (trade, swap, etc) any bitcoin for goes back onto the buy-side of the market at a lower price than it was sold for.
By the time 21 million dollars worth of bitcoin had been bought, every bitcoin ever ultimately to be minted would have been "worth as proven by total global buy-side offers" one dollar minus whatever "re-stocking fee" or "human-side transaction fee plus protocol-implemented fee" had been applied.
On the markets as represented by buy side vs sell side order-books, that "human-side transaction fee" would express itself or be represented by/as the "spread" between the top of the column of buy-offers and the bottom of the column of sell-offers.
Aha but wait, suppose instead of implementing the "put the proceeds of bitcoin sales back onto the buy-side" as a "buy wall" per sale of bitcoins, the miners used my "columns rather than walls" approach, building columns of buy offers all the way from the lowest price the exchange allows upward?
Gosh, in that case depending on the granularity of pricing the exchanges support one extreme could be along the lines of oh look the first dollar spent on bitcoin just happened, that means we can put maybe 20 million buy offers in place, all the way up from 1/21M dollars to 20M/21M dollars or higher depending on granularity one could spread almost one whole dollar across.
The "twist" rears its head around this point or so, the "twist" being that bitcoin turns out to be more along the lines of a commodity than of money; it is unfortunately quite ridiculously expensive to try to use it as money in the sense of money-as-IOUs.
Even using inscription to inscribe satoshis as money tokens it isn't cheap.
So how can the miners - the issuers of the bitcoins if indeed bitcoins are to function as money rather than as commodities - "redeem" their IOUs?
In the normal course of usage of IOUs, presumably in fair trade (oops is fair trade at all normal, maybe put that aside for now) the amount the miners traded the IOUs for is presumably at least somewhere vaguely near the amount of debt they incurred by issuing IOUs?
It all gets very awkward and murky and cloudy trying to reward the miners for issuing IOUs, which is to say, for going into debt.
Supposedly that is not what they are intended to be rewarded for though, is it?
The intent was to reward them for securing the blockchain. For keeping track, in other words, of their IOUs as they change hands over and over and over again.
Which normally with IOUs would only happen up until they arrive back in the hands of their issuer.
Once the issuer has redeemed (bought back) all of their IOUs, they are out of debt.
The massive expense of Proof of Work really makes that entire picture very problematic.
Nowadays there are far far cheaper means that purport to secure blockchains.
So run through that whole picture again, leaving out the "need" for "miners" (the issuer of the IOUs, singular or collective) to expend ridiculous sums on massive expenses just to get the darn IOUs issued and keep them legible long enough to return into the hands of the issuer.
Now hopefully it has become clear that stability should be achievable by a vigilant issuer that also acts as a wise and capable market-maker.
Whether that entity is singular or collective should only alter its own internal politics / ability to act as it supposedly intended to act or as it was designed to cause its own constituents to act or however you prefer to phrase that kind of concept.
Provided the issuer does not deviate from using the proceeds of the sale or trade of the issued IOUs (tokens, coins whatever terminology) to strengthen the buy-side, and puts them up for sale as a column of sell offers ascending way up into the stratosphere, many times as high as in their wildest dreams they imagine it could possibly go (so that they will never be "cleaned out" with none left to put on sale if ever someone does somehow manage to buy the entire column, it should always remain possible to to keep its value up to its "face value" (the amount of debt it represents).
A powerful thing that arises from the above is that in reality it need not be only the issuer who performs this strategy of market-making.
In my experience, applying it in cases such as BTC/IXC and BTC/I0C, long term the strategy tends to accumulate more and more and more of the sell-side (the IOU side, if you will, rather than the commodity or hard-currency side that is the BTC) even while taking profit from time to time by thinning out the column of BTC-side buy offers.
So even given an already existing specie, it seems it would be "just a matter of time" for a market-maker operating that strategy to take off of the market all extant specie of the sell side species.
Once having taken them off the market, one need not even burn them on behalf of the issuer to relieve them of the debt they represent; one could re-issue them oneself, that is, put them back up for sale.
Money mostly works because all or almost all of those spending are almost equally as willing to work for or trade for it; unlike barter of dis-similar items a huge part of the point of money is both parties to a trade agree as to its value; that is afterall how folks get caught into the delusion that it is "stable"!
-MarkM-
