When Lehman went bankrupt, the net asset value (NAV) of the Reserve Primary Fund "broke the buck", falling to 97 cents. This ignited a run on money market funds, disrupting credit flows and deepening the crisis. Money market funds invest in short-term debt like commercial paper, and the run caused short-term credit markets to dry up suddenly. This was in the process of causing a complete meltdown when the U.S. Treasury stepped in to insure that NAVs would be restored to $1.
The incentive to run is due to investors being guaranteed a stable $1/share. When a fund breaks the buck, the first redeemers get their $1 back while the last redeemers absorb all the losses when the money runs out. If the $1 guarantee is removed, investors share whatever losses equally and the incentive to run goes away.
We can't rely on the U.S. Treasury to guarantee everything. There is ~$3.5TR in money market funds. If investors can't handle a small chance of small losses, they shouldn't invest in these funds.