The vacuum persistence probability, encoded in the imaginary part of the in-out effective action, is a basic measure of vacuum instability and particle production. However, its evaluation may appear prescription-dependent: the Bogoliubov prescription and the Green’s function prescription can yield different results. This discrepancy reflects the incomplete treatment of the endpoint vacuum states in the conventional Green’s function reconstruction of the effective action. We establish a boundary-completed reconstruction that consistently incorporates the bulk Green’s function and the endpoint vacuum contributions, thereby determining the structure of the complete in-out effective action. The resulting vacuum persistence probability is uniquely determined and agrees with the Bogoliubov result.