The capture of a soft spherical particle in a rectangular slit leads to a nonmonotonic pressure-flow rate relation at low Reynolds number. Simulations reveal that the flow induced deformations of the trapped particle focus the streamlines and pressure drop to a small region. This increases the resistance to flow by several orders of magnitude as the driving pressure is increased. As a result, two regimes are observed in experiments and simulations: a flow-dominated regime for small particle deformations, where flow rate increases with pressure, and an elastic-dominated regime in which solid deformations block the flow.