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. The exposure to sectors most hurt by the COVID-19 crisis was also important. 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. The impact materialized quickly after announcement and was large over the post-crisis period among funds that held bonds eligible for purchase. In turn, the Fed bond purchase program had spillover effects, stimulating primary market bond issuance by firms whose outstanding bonds were held by the impacted funds and stabilizing peer funds whose bond holdings overlapped with those of the impacted funds. The evidence points to a new “bond fund fragility channel” of the Federal Reserve liquidity backstop whereby the Fed bond purchases transmit to the real economy via bond funds.