Stablecoins are usually tokens that are built on the Ethereum or Tron network. So they are dependent on the main coin and its blockchain - especially on the network security, scalability, fees, and transaction speeds. I just would like to say, that you simply can´t use stablecoins without the altcoin and its blockchain for now. There is no stablecoin that uses its own blockchain and probably that's good because it is much easier for the users, to hold them on one Ethereum wallet.