The purpose of this paper was to clarify the physical reason for the previously reported experimental results that a complete breakdown in a silicone-oil/PET-film composite for a negative point occurred after a considerable time had elapsed after the film breakdown due to charge deposition. It was concluded from some experiments that the breakdown in the composite was completed by a positive streamer propagation from the breakdown spot of the film which was induced by negative charges emitted from the point cathode immediately after the film breakdown. The minimum delay time between the complete breakdown and the film breakdown was approximately equal to the transit time of negative charges from the point cathode to the film.