We introduce damage intelligent soft-bodied systems via a network of self-healing light guides for dynamic sensing (SHeaLDS). Exploiting the intrinsic damage resilience of light propagation in an optical waveguide, in combination with a tough, transparent, and autonomously self-healing polyurethane urea elastomer, SHeaLDS enables damage resilient and intelligent robots by self-healing cuts as well as detecting this damage and controlling the robot's actions accordingly. With optimized material and structural design for hyperelastic deformation of the robot and autonomous self-healing capacity, SHeaLDS provides reliable dynamic sensing at large strains (ε = 140%) with no drift or hysteresis, is resistant to punctures, and self-heals from cuts at room temperature with no external intervention. As a demonstration of utility, a soft quadruped protected by SHeaLDS detects and self-heals from extreme damage (e.g., six cuts on one leg) in 1 min and monitors and adapts its gait based on the damage condition autonomously through feedback control.