This study develops and analyzes a nonlinear dynamical model describing the coupled evolution of corruption, organized crime, and cybercriminality under the influence of institutional trust, economic stress, and digital transparency. Unlike traditional enforcement-driven frameworks, the proposed model incorporates endogenous feedback between corruption prevalence and institutional trust, allowing corruption to both erode and be amplified by governance quality. Economic stress is introduced as a recruitment amplifier, while digital transparency functions as a structural suppression mechanism. The model is formulated as a system of nonlinear ordinary differential equations and rigorously examined. We establish positivity, boundedness, and the existence of a positively invariant region. Using the next-generation matrix approach, a modified basic reproduction number is derived that explicitly incorporates trust erosion and transparency effects. Local and global stability of the crime–corruption–free equilibrium are proven via Lyapunov techniques. Furthermore, center manifold analysis demonstrates the potential for backward bifurcation, indicating governance tipping thresholds and multi-stability regimes. An optimal control framework is constructed to determine cost-effective strategies combining transparency investment, prosecution intensity, and employment stabilization policies. Numerical investigations calibrated to India-specific governance and crime indicators illustrate how strengthening institutional trust and digital transparency can produce nonlinear reductions in corruption prevalence. The findings provide analytically grounded insights for sustainable governance reform in digitally evolving socio-economic systems.