Advanced synthetic materials are needed to produce nano- and mesoscale structures that function autonomously, catalyze reactions, and convert chemical energy into motion. This paper describes supracolloidal fiber-like structures that are composed of self-adhering, or "sticky," oil-in-water emulsion droplets. Polymer zwitterion surfactants serve as the key interfacial components of these materials, enabling multiple functions simultaneously, including acting as droplet-stabilizing surfactants, interdroplet adhesives, and building blocks of the fibers. This fiber motion, a surprising additional feature of these supracolloidal structures, is observed at the air-water interface and hinged on the chemistry of the polymer surfactant. The origin of this motion is hypothesized to involve transport of polymer from the oil-water interface to the air-water interface, which generates a Marangoni (interfacial) stress. Harnessing this fiber motion with functional polymer surfactants, and selection of the oil phase, produced worm-like objects capable of rotation, oscillation, and/or response to external fields. Overall, these supracolloidal fibers fill a design gap between self-propelled nano/microscale particles and macroscale motors, and have the potential to serve as new components of soft, responsive materials structures.