Minimal Structural Sufficiency (F_{min}) defines the critical threshold where neural networks undergo irreversible collapse during pruning, regardless of remaining capacity. This study proves that stability depends on preserving invariant structural supports rather than simple parameter density. Beyond this boundary, the model experiences a non-linear failure in operational performance (Psi) that cannot be recovered through retraining. By introducing the Invariant Structural Support Principle (ISSP), the research explains why architectural coherence is lost once the dominant spectral modes are disrupted, providing a new framework for understanding model resilience and catastrophic degradation.