This is an important distinction. When the money marketeer redeems a dollar for less than a dollar it "Breaks the Buck" [0]. Cowen's MM account IIRC was the first one to do that back during the 01 crash.
Yeah. And the haircut is usually quite small. If I sold my money market for 98 cents on the dollar in a financial crisis I really wouldn't be that upset.
[0] https://www.investopedia.com/terms/b/breaking-the-buck.asp