In the decade following the financial crisis of 2008, investment funds in corporate bond markets became prominent market players and generated concerns of financial fragility. The COVID-19 crisis provides an opportunity to inspect their resilience in a major stress event. Using daily microdata, we document major outflows in these funds during this period, far greater than anything they experienced in past events. Large outflows were sustained over several weeks and were widespread across funds. Inspecting the role of sources of fragility, we show that both the illiquidity of fund assets and the vulnerability to fire sales were important factors in explaining outflows in this episode. The exposure to sectors most hurt by the COVID-19 crisis was also important. Two policy announcements by the Federal Reserve about extraordinary direct interventions in corporate-bond markets seem to have played an important role in calming down the panic and reversing the outflows.