The obligation density framework has identified the termination coefficient T(t) ∈ [0,1] as the variable measuring whether discharge mechanisms exist that can clean-close obligations on a given participant. This paper proves a structural theorem connecting an observable institutional pipeline — the STAR (Surveillance, Tagging, Aggregation, Reporting) behavioural-classification system as documented in compliance, risk-vendor, and EMI architectures — to individual-layer T(t) collapse. We define the STAR Pipeline Obligation Operator and identify three structural conditions (event trigger; recursive expansion; absent discharge) that characterise STAR-class systems. We prove the STAR-OD Theorem: any behavioural-classification system satisfying the three conditions drives the participant’s termination coefficient to zero, the effective obligation density to infinity, and a threshold-crossing exclusion event becomes inevitable under sustained engagement.