EOS stable coins are the mapping of major blackchain assets on the EOS.IO network. Users who hold major blockchain assets are able to swap their assets from the original bockchain network to the EOS.IO network through our gateway service, so as to utilize them in DAPPs or decentralized exchanges. EOS stable coins enrich the diversity of the EOS ecosystem and offer a convenient way for users from other blockchain networks to experience the EOS world.
The volume of stable coins in circulation is always equal to the volume of the original assets. The gateway provides a 24/7 two-way swap service; users can swap their stable coins back to the original blockchain at will. Therefore, the stable coins achieve a stable 1:1 pegging relationship with the original network assets.
Source: https://medium.com/@dice1/bitpie-cross-chain-stable-coins-more-details-3801b772e105
The stablecoin isn't completely on EOS. EOS acts like a much cheaper and efficient version of Lightning Network other coins such as USDT. At least that's how things are for the time being.