Stretchable electronics based on inorganic materials are an innovative technology with potential applications for many emerging electronic devices, due to their combination of stretchable mechanics and high electronic performance. The compliant elastomeric substrate, on which the brittle electronic components are mounted, plays a key role in achieving stretchability. However, conventional elastomeric substrates can undergo excessive mechanical deformation, which can lead to active component failure. Here, we introduce a simple and novel strategy to produce failure-resistant stretchable electronic platforms by bonding a thin film of stiff material, patterned into a serpentine network layout, to the elastomeric substrate. No prestraining of the substrate is required, and these systems offer sharp bilinear mechanical behavior and high ratio of tangent-to-elastic moduli. We perform comprehensive theoretical, numerical, and experimental studies on the nonbuckling-based prestrain-free design, and we analyze the key parameters impacting the mechanical behavior of a strain-limiting substrate. As a device-level demonstration, we experimentally fabricate and characterize skin-mountable stretchable copper (Cu) electrodes for electrophysiological monitoring. This study paves the way to high performance stretchable electronics with failure-resistant designs.