When brushes of flexible fibers are removed from liquid baths, these brushes sometimes show unwanted droplets at their ends, depending on the length, rigidity and shape of their fibers. Capillary forces arising from the varying cross-sections of conical fiber tips have been thought to eliminate the droplets. However, these forces may not operate with water, which fills the entire space between the fibers of a brush. Here, we theoretically show that brushes eliminate unwanted droplets with a physical mechanism that is significantly different from a single conical fiber by 'closing' their ends. We analyze the hydrostatics of water in a brush when it is removed from a bath, and we identify the condition under which the end of the brush is closed, emphasizing the roles played by the elastic deformation of the flexible fibers owing to interfacial forces. Moreover, this theory predicts that the volume of water that is captured by brushes is a non-monotonic function of the length of their fibers because the fibers show excluded volume interactions when their ends are 'closed'. This theory may guide the design of liquid-transfer devices that can retain liquids in a controlled manner.