Elastomer composites with stable electrical conductivity are crucial for the reliable operation of advanced flexible electronic devices under temperature variations or various deformations. However, current materials struggle to simultaneously maintain stable conductivity during significant thermal shocks or mechanical deformations. To address this challenge, we propose a general strategy for constructing temperature/deformation-insensitive conductive pathways by leveraging a liquid metal (LM)/polymer bicontinuous phase network. Based on the communicating vessel-like structure of the material, the material enables self-adaptive interfacial void filling through solid–liquid cooperative deformation mechanisms, thereby maintaining conductive pathways under elevated temperatures or mechanical strains. At low temperatures, the LM undergoes expansion to establish new conductive channels, which reduces the material’s electrical resistance and ensures excellent conductivity in cryogenic environments. As a proof of concept, the elastomer exhibits exceptional and stable conductivity (σ_{298 K} = 500 S/cm) under drastic thermal shocks (ΔT = 410 K). Furthermore, the material demonstrates minimal resistance variation under diverse deformations, with only a 1.2% increase in resistance under 170% tensile strain. Additionally, the composite maintains nearly invariant ultra-broadband electromagnetic shielding performance and stable thermal conductivity at elevated temperatures. This work provides a strategy for the design and fabrication of flexible conductive elastomers capable of stable operation in complex extreme environments.