A non-woven fiber assembly comprises one or more fibers containing an adhesive component, an elastomeric component, and a hydrophilic component. A method of making a non-woven fiber assembly comprises the steps of providing one or more fiber-forming materials comprising an adhesive component, an elastomeric component, and a hydrophilic component, and forming said one or more fiber-forming materials into at least one fiber. A method of treating a patient comprises applying a medical dressing comprising the fiber assembly of the present invention to a patient. An apparatus (10) for forming a non-woven fiber assembly comprises a plurality of reservoirs (12, 16, 20) for containing more than one type of fiber-forming material, a plurality of valves (14, 18, 22), each independently in communication with a reservoir, and a fiber-forming device (28) selected from the group consisting of a spinnerette, a NGJ nozzle, and an electrospinning device, in communication with the valves.