A flexible fiber carrying a liquid drop may coil inside the drop thereby creating a drop-on-fiber system with an ultra-extensible behaviour. During compression, the excess fiber is spooled inside the droplet and capillary forces keep the system taut, while during elongation, the fiber is gradually released and if a large number of spools is uncoiled a high stretchability is achieved. This mechanical behaviour is of interest for stretchable connectors but information, may it be electronic or photonic, usually travels through stiff functional materials and high Young's modulus, leading to large bending rigidity, prevents in-drop coiling. Here we overcome this limitation by attaching a beam of soft elastomer to the functional fiber, thereby creating a composite system which exhibits in-drop coiling and carries information while being ultra-extensible. We present a simple model to explicate the underlying mechanics of the addition of the soft beam and we show how it favors in-drop coiling. We illustrate the method with a two-centimeter long micronic PEDOT:PSS conductive fiber joined to a PVS soft beam, showing the system conveys electricity throughout a 1900% elongation.