Detailed Description This paper introduces a unified framework for understanding, classifying, and monitoring system failure across engineering, medicine, ecology, economics, and complex adaptive systems. The work establishes a fundamental bifurcation between two distinct classes of collapse: cumulative collapse and coercive collapse. Cumulative collapse arises through progressive internal structural degradation and generates detectable precursor signals before failure. Coercive collapse, by contrast, occurs when external forcing exceeds structural reserve capacity in a manner that leaves no measurable internal warning signature. The study demonstrates that this distinction is not merely practical but reflects an underlying information-theoretic constraint on predictability. Building on the structural continuity principles of Union Dipole Theory (UDT), the paper develops and validates a remarkably simple monitoring quantity: Rate(L) = d(EMA(L))/dt where L represents a normalized structural-health proxy and EMA denotes an exponentially weighted moving average. Extensive multi-physics simulations show that Rate(L) functions as a minimal sufficient statistic for the detection of cumulative failure processes. The framework is evaluated across multiple physically distinct failure classes, including regime-shift systems, latent-state systems, oscillatory degradation systems, shock-driven systems, and fatigue-driven coercive failures. Results from ten-seed robustness studies demonstrate consistent early-warning capability for cumulative failures while confirming the theoretical impossibility of advance warning for purely coercive collapse events. Direct comparisons against canonical Critical Slowing Down (CSD) indicators, including lag-1 autocorrelation and rolling variance, reveal substantial advantages of the Rate(L) approach in hidden-state and oscillatory environments. The study further introduces a Unified Safety Protocol (USP) that prescribes a classification-first strategy: identify the failure class before selecting monitoring, resilience, or intervention methods. Beyond its practical implications, the work argues that failure taxonomy is more fundamental than indicator design. Rather than seeking a universal early-warning indicator, the paper proposes that predictive success depends on recognizing whether the underlying process belongs to the cumulative or coercive class. The methodology is fully reproducible, includes statistical robustness testing, threshold-sensitivity analysis, ablation studies, and explicit benchmarking against established monitoring approaches. Potential applications span predictive maintenance, structural health monitoring, process safety, healthcare diagnostics, environmental management, infrastructure resilience, governance monitoring, and complex-system risk assessment. This publication forms part of the broader Structural Continuity research program and provides a practical operational bridge between theoretical continuity principles and deployable early-warning systems.