How stablecoin maintains its price to 1$
The trick that all stablecoins use behind maintaining their price to 1$ is to adjust their supply based on demand.
Actually the price of a stablecoin can go above a dollar, when the crypto market crash. More precisely, It happens when everyone rush to protect their portfolios from further losses by selling their cryptos in returns of a stablecoin. Which causes a high demand for buying the stablecoin.
Conversely, when people start selling their stablecoins, to buy whichever crypto that is going to the moon. This sometimes pushes the price of the stablecoin bellow a dollar. When this happens, The stablecoin is burned to reduce the supply and increase the price to reach 1$
What would happen if everyone would need to cash out digital dollars to physical dollars?
Black swan event
In theory, The companies which issue the Fiat stablecoin generally claim that they have the equivalent amount of dollars in the bank to back the tokens in circulation across all cryptocurrencies’s Blockchains.
When the fiat stablecoins are minted, this means that someone went to the company behind that stablecoin and gave them dollar in exchange of tokens which are then put into circulation.
When the fiat stablecoins are burned, this means that someone went to the company behind that stablecoin and gave them tokens in exchange for dollars, Which than take those dollars out of circulation.
This ration 1:1 of dollars to the token is extremely important because if there was ever a black swan event, which means everyone want to cash out their cryptocurrencies in exchange of dollars.
Not having a sufficient amounts of dollars in the bank, means not everyone would be able to convert their digital dollars into physical dollars.