Conservation Closure for Finite Spacetime Endpoints: Distributional Defects, No-Extinction Bounds, and Boundary Requirements

A claim that a physical system terminates its spacetime realization after a finite interval is stronger than loss of detectability, causal disconnection, geodesic incompleteness, breakdown of a mathematical description, or ordinary conversion into other spacetime-supported products. This paper analyzes such a claim as an endpoint-closure problem. For charged and massive point carriers, finite worldline truncation produces distributional current and four-momentum endpoint defects; abrupt termination of an extended stress-energy field produces a surface-supported normal-flux defect. For an isolated locally integrable matter-plus-fields system in Minkowski spacetime with conserved total stress-energy, no flux at spatial infinity, complete stress-energy accounting, and positive conserved pre-terminal energy, complete finite-time extinction of future total stress-energy support is incompatible with these assumptions. The paper further analyzes possible compensating distributions, shows the limits of compact and point-supported closure, gives an explicit higher-order noncompact counterexample to an unrestricted no-compensator claim, and connects the result with curved-spacetime vacuum-conservation theorems and boundary closure. No universal impossibility theorem or physical transition mechanism is claimed. The main result is a bounded endpoint-closure framework in which a viable finite terminal-history law must supply both event-generation dynamics and physical balance completion.