Aerogels combine ultralow density with high surface area, yet their brittle, open networks preclude tensile deformation and hinder integration into wearable electronics. Here we introduce a prestrain-enabled coaxial architecture that converts a brittle conductive aerogel into a highly stretchable fiber. A porous thermoplastic elastomer (TPE) hollow sheath is wet-spun using a sacrificial lignin template to ensure solvent exchange and robust encapsulation. Conductive polymer-based precursor dispersions are infused into prestretched TPE tubes, frozen, and lyophilized; releasing the prestretch then programs a buckled aerogel core that unfolds during elongation without catastrophic fracture. The resulting TPE-wrapped aerogel fibers exhibit reversible elongation up to 250% while retaining electrical function. At low strains (<60%), resistance changes are small and stable (ΔR/R0 < 0.04); at larger strains the response remains monotonic and fully recoverable, enabling broad-range sensing. The mechanism is captured by a strain-dependent percolation model in which elastic decompression, contact sliding, and controlled fragmentation/reconnection of the aerogel network govern the signal. This generalizable strategy decouples elasticity from conductivity, establishing a scalable route to ultralight, encapsulated, and skin-compatible aerogel fibers for smart textiles and deformable electronics.