The primary risk of collateralized stablecoins is that holders will lose the ability to redeem the stablecoin at a 1:1 ratio for the underlying asset. If that occurs, the value of the stablecoin will fall below the 1:1 ratio (this is called “price decoupling”). Holders of the stablecoin would still be able to send it from one cryptocurrency wallet to another cryptocurrency wallet, but they would not be able to redeem it on an exchange for the underlying asset and merchants would not accept it for payment.
The risk of price decoupling exists because the issuers of stablecoins that hold the underlying asset in reserve are centralized entities that are subject to all the risks of the fiat currency financial system. The two most likely causes would be fraud by the issuer of the stablecoin (whereby the issuer issues more stablecoins than the amount of the underlying asset held in reserve) or interference by the bank that holds the underlying asset (most likely due to coercion by the government that regulates the bank).
Algorithmic stablecoins have additional risks associated with their blockchain smart contract functionality. These risks include disruption of the automated price stabilization mechanism and, in some cases, the potential of funds being locked by the stablecoin issuer.