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 corporate-bond funds during the COVID-19 crisis. Large outflows were sustained over weeks and most severe for funds with illiquid assets, vulnerable to fire sales, and exposed to sectors hurt by the crisis. By providing a liquidity backstop for their bond holdings, the Federal Reserve bond purchase program helped to reverse outflows especially for the most fragile funds. In turn, the program had spillover effects on primary market issuance and peer funds. The evidence points to a “bond-fund fragility channel” whereby the Fed liquidity backstop transmits to the real economy via funds.