We study the shape of the relationship between French bond mutual funds' returns and their flows by using Datastream data on the period 2005-2017. Beyond considering the effect of relative performance, we also study the effects of absolute short-term returns on funds' flows. We find empirical evidence of a mechanism proving that mutual funds can be at the origin of financial instability. Indeed, the possibility that negative shocks impacting the short-term returns generate outflows can result in a loop between funds' flows and their returns. Our model authorizes the presence of nonlinear effects in the shape of the relationship between flows and performances. The results demonstrate that mutual funds presenting very negative short-term returns experience superior outflows compared to funds presenting less negative short-term returns (this effect appears at the bottom negative return quintile). Conversely, this nonlinear effect is not present on the positive short-term returns' segment. Irrespective of mutual funds' returns, the investors seem to redeem more during periods of financial stress. Additional results show that for institutional investors (which are here defined as the owners of the biggest shares and thus whose decisions will pose more for the mutual fund), the nonlinear effect appears starting with the second negative return quintile. We hence confirm the presence of a potential source of fragility and risk coming from negative shocks on bond mutual funds' short-term returns.