This is a bank run in the sense that there is a mismatch in maturities, and thus a money fund is a "virtual bank": the assets of money funds, while short term, nonetheless typically have maturities of several months, while investors can request redemption at any time, without waiting for obligations to come due. Thus if there is a sudden demand for redemptions, the assets may be liquidated in a fire sale, depressing their sale price.
The Money Market enables the commercial banks to use their excess reserves in profitable investment. The main objective of the commercial banks is to earn income from its reserves as well as maintain liquidity to meet the uncertain cash demand of the depositors. In the money market, the excess reserves of the commercial banks are invested in near-money assets (e.g., short-term bills of exchange), which are easily converted into cash. Thus, commercial banks earn profits without sacrificing liquidity.