Particle-laden gravity flows, called turbidity currents, flow through river-like channels across the ocean floor. These submarine channels funnel sediment, nutrients, pollutants and organic carbon into ocean basins and can extend for over 1000's of kilometers. Upon reaching the end of these channels, flows lose their confinement, decelerate, and deposit their sediment load; this is what we read in textbooks. However, sea floor observations have shown the opposite: turbidity currents tend to erode the seafloor upon losing confinement. Here we use a state-of-the-art scaling method to produce the first experimental turbidity currents that erode upon leaving a channel. The experiments reveal a novel flow mechanism, here called flow relaxation, that explains this erosion. Flow relaxation is rapid flow deformation resulting from the loss of confinement, which enhances basal shearing of the turbidity current and leads to scouring. This flow mechanism plays a key role in the propagation of submarine channel systems.