In theory it should be impossible to fall apart as long as they aren't actively trying to scam people, in practice very few of these stable coins publish 3rd party audits showing they actually have the money to back deposits, maybe this will be different.
How it works is when someone buys $100 worth of NZDD coin, they put that $100 in a bank account and issue 100 coins. Someone sells 100 coins back to them, they burn the coins (send them to a null wallet to be lost forever) and withdraw $100 from their account. Basically as long as they aren't spending more administrating the coin than they can earn back from investments with people's deposits they are in the green (the cash appreciates, the coins don't)
As long as they don't do anything stupid with the real money (e.g. let a 26 year old attempt to learn how to run a high frequency trading firm with it (FTX), gamble/piss it all away and then fake your own death (QuadrigaCX), or run a super fractional reserve with illiquid investments that could cause you to go tits up if any news ever spurs a bank run (Silicon Valley Bank)