Conductive elastic composites have been used widely in soft electronics and soft robotics. These composites are typically a mixture of conductive fillers within elastomeric substrates. They can sense strain via changes in resistance resulting from separation of the fillers during elongation. Thus, most elastic composites exhibit a negative piezoconductive effect, i.e. the conductivity decreases under tensile strain. This property is undesirable for stretchable conductors since such composites may become less conductive during deformation. Here, we report a liquid metal-filled magnetorheological elastomer comprising a hybrid of fillers of liquid metal microdroplets and metallic magnetic microparticles. The composite's resistivity reaches a maximum value in the relaxed state and drops drastically under any deformation, indicating that the composite exhibits an unconventional positive piezoconductive effect. We further investigate the magnetic field-responsive thermal properties of the composite and demonstrate several proof-of-concept applications. This composite has prospective applications in sensors, stretchable conductors, and responsive thermal interfaces.