The preparation of intelligent structures for multiple smart applications such as soft-ro-botics, artificial limbs, etc., is a rapidly evolving research topic. In the present work, the preparation of a functional fabric, and its integration into a soft elastomeric matrix to develop an adaptive fiber-elastomer composite structure, is presented. Functional fabric, with the implementation of the shape memory effect, was combined with liquid polybutadiene rubber by means of a low-temperature vulcanization process. A detailed investigation on the crosslinking behavior of liquid polybutadiene rubber was performed to develop a rubber formulation that is capable of crosslinking liquid rubber at 75 °C, a temperature that is much lower than the phase transformation temperature of SMA wires (90–110 °C). By utilizing the unique low-temperature crosslinking protocol for liquid polybutadiene rubber, soft intelligent structures containing functional fabric were developed. The adaptive structures were successfully activated by Joule heating. The deformation behavior of the smart structures was experimentally demonstrated by reaching a 120 mm bending distance at an activation voltage of 8 V without an additional load, whereas 90 mm, 70 mm, 65 mm, 57 mm bending distances were achieved with attached weights of 5 g, 10 g, 20 g, 30 g, respectively.