Stretchable composites comprising liquid metal (LM) inclusions and silicone elastomers (LME composites) are of great interest in the design of soft electronic and wearable devices. Soft conductors consisting of highly deformable materials and low ratio of conductive fillers offer high stretchability and good strain-tolerant conductance while not compromising the functionality of their host systems. Despite advances, actively achieving electrical conductivity for LME composites with a low ratio of conductive fillers is challenging, especially in highly deformable soft elastomers. This work introduces a new fabrication strategy that turns non-conductive LME composites with highly deformable elastomers into conductive ones using a small amount of magnetic conductive fillers (e.g., Nickel particles and LM droplets). By actively manipulating conductive fillers with an external magnetic field, the new composite can sustainably achieve electrically conductive traces at any desired locations. Experimental results show that the new LME composite can achieve high conductivity of 2.55 x 105 S m-1, high stretchability of over 450%, good strain-tolerant conductance (R/R0 ~ 1.56 at 250% strain), and especially a tensile modulus as low as 60.1 kPa at a very low loading ratio of conductive filler (9.7% by volume). The non-contacting magnetic fabrication also enables the creation of diverse configurations in 1D, 2D, and 3D forms, offering a broad range of potential applications from stretchable electronics, wearable devices, smart garments, to biomedical systems.