Breathable residual-limb system that admits air and allows sweat to evaporate from the surface of the residual limb. In an embodiment, the system comprises a liner sock to be worn on the residual limb, and comprising air-permeable textile forming a substantially cylindrical portion that is closed on a distal end and open on a proximal end and comprising an internal surface and an external surface. The liner sock further comprises a friction-interface material that covers only a portion of the internal surface of the air-permeable textile, such that, when worn on the residual limb, the friction-interface material contacts a surface of the residual limb, and an uncovered portion of the air-permeable textile which the friction-interface material does not cover allows air to pass between an external environment of the liner sock and the surface of the residual limb.