The mechanism of DAI is quite a bit different. If the value of the underlying collateral crashes the created DAI is destroyed, which raises the value of DAI from its peg [1]. The only scenario in which DAI depegs in a direction against DAI holders is if the underlying collateral (i.e. Ethereum) flash crashes before anyone can liquidate the minted DAI.
[1] https://makerdao.com/en/whitepaper#maker-protocol-auctions