This paper introduces a proposal for money market fund (MMF) reform that could mitigate systemic risks arising from these funds by protecting shareholders, such as retail investors, who do not redeem quickly from distressed funds. Our proposal would require that a small fraction of each MMF investor's recent balances, called the "minimum balance at risk" (MBR), be demarcated to absorb losses if the fund is liquidated. Most regular transactions in the fund would be unaffected, but redemptions of the MBR would be delayed for thirty days. A key feature of the proposal is that large redemptions would subordinate a portion of an investor's MBR, creating a disincentive to redeem if the fund is likely to have losses. In normal times, when the risk of MMF losses is remote, subordination would have little effect on incentives. We use empirical evidence, including new data on MMF losses from the U.S. Treasury and the Securities and Exchange Commission, to calibrate an MBR rule that would reduce the vulnerability of MMFs to runs and protect investors who do not redeem quickly in crises.