Actually there isn't a true stable coin, fiat or crypto.
However, in my perspective, a true stable-coin is exactly what we need, and I'm waiting keen for someone who will be able to implement that kind of feature in the near future, It is probably the missing brick in the Nakamoto vision.
The most fascinating model I've ever seen in that field, is a kind of Hayek double coin system backed by an external "cryptoasset" as reserve asset. Essentially a double coin system made by a stable coin tethered to a reference basket, and a share coin, offered by an IPO and paid by whatever the best external crypto-asset would be available (actually, bitcoin).
The share-holders would be, in fact, a sort of DAO, acting as a Decentralized Reserve Asset Bank, keeping the stable-coin tethered to the reference basket by using the bitcoin reserve, obviously everything being regulated by an immutable, permissionless, distributed ledger's protocol/algorithms.
That kind of stable-coin would be emitted or bought by the the DRAB to keep its purchasing power in a predefined channel with the reference basket. The shares would be backed by bitcoins, so that, the asset, will be used for its primary essence. Also, new shares, should be emitted in exchange of bitcoins, thus increasing the BTC asset reserve of the DRAB, but not diluting the shares.
In this scheme, the protocol proposed for the distributed ledger consensus, by some of its supporters, would be something called "proof of payment", where "miners" would use the external crypto asset (bitcoin) to concur for the Block Validations, by offering a rational asset amount (compared to the share price), exactly as a POW-miner offers his hashing power and electricity in a POW protocol.
All the bitcoins spent for that, will be not burnt like in a Proof-of-Burn protocol, but will simply go to increase the asset reserve of the DRAB.
Anyone would be able to build up his System, as is to create a new "cryptocurrency", but by an IPO, so investing his own funds and not using money from others as with any sorts of ICOs or crowds.
In fact, the validity of the reference basket (that the DRAB should be able to change and regulate in some way) and the team, building up and advertising a good platform, should be, really, the major factors for the success of any of those "Hayek systems".
Non-fungibility between the 2 coins, an asset reserve made by an external crypto-commodity, as well as the proof-of-payment idea, are the main features of this concept.
This scheme could be extended (with some obvious differences) as well to actual fiat central banks, in some way replicating a gold standard 2.0: a CriptoGold standard. The reference basket would be than the fiat currency of that central bank, with probably no need for shareholders, and, probably, fast transactions and low fees would be the major resting features of what the cryptos offers.....but the external reserve asset, BTC in this case, should gain value and would not be in exponential need for scaling, as well as the share-coin, because the stable-coin would cover that need.
Some experts say that Hayek theory is in contrast with the BTC revolution despite some evident similarities, and with good reasons: because of its non-fungibility, scarcity, thus extreme volatility and lack of unit of account. The non inter-fungible Double coin idea backed by an external crypto asset, would make the Hayek dream of healthy competition between privates money systems possible, and open the route for even extremely different visions of a monetary cultural shift.