it depends on how you define "being frozen" (since you mention exchanges).

when you deposit some coins (whether it is stablecoin or anything else including bitcoin) to an address provided to you by an exchange you do not own that address, you only own an account and the exchange owns the address while letting you access a number in their database representing how much you deposited.
obviously they can freeze your "account" if you deposit coins that they don't like. this affects everything from bitcoin to stablecoins, tokens, shitcoins,...

but when you send coins to an address that you and you alone control (created the private key locally and store it that way) then whether it could be frozen or not depends on whether the coin is centralized or not. for example nobody can ever freeze bitcoin coins. but when the coins are centralized, they are like accounts (exchange account or a bank account) and the centralized authority can easily freeze them or even move the coins.
all stablecoins that i have seen so far (that are in use and are stable) are centralized.