Compared with the large plastic deformation observed in ductile metals and organic materials, inorganic semiconductors have limited plasticity (<0.2%) due to their intrinsic bonding characters, restricting their widespread applications in stretchable electronics. Herein, the solution‐processed synthesis of ductile α‐Ag2S thin films and fabrication of all‐inorganic, self‐powered, and stretchable memory devices, is reported. Molecular Ag2S complex solution is synthesized by chemical reduction of Ag2S powder, fabricating wafer‐scale highly crystalline Ag2S thin films. The thin films show stretchability due to the intrinsic ductility, sustaining the structural integrity at a tensile strain of 14.9%. Moreover, the fabricated Ag2S‐based resistive random access memory presents outstanding bipolar switching characteristics (Ion/Ioff ratio of ≈105, operational endurance of 100 cycles, and retention time >106 s) as well as excellent mechanical stretchability (no degradation of properties up to stretchability of 52%). Meanwhile, the device is highly durable under diverse chemical environments and temperatures from −196 to 300 °C, especially maintaining the properties for 168 h in 85% relative humidity and 85 °C. A self‐powered memory combined with motion sensors for use as a wearable healthcare monitoring system is demonstrated, offering the potential for designing high‐performance wearable electronics that are usable in daily life in a real‐world setting.