This paper completes the studies undertaken in [3, 4] and [8], where the authors quantify the impact of a random time on the No-Unbounded-Risk-with-Bounded-Profit concept (called NUPBR hereafter) for quasi-left-continuous models and discrete-time market models respectively. Herein, we focus on the NUPBR for semimartingales models that live on thin predictable sets only and when the extra information about the random time is added progressively over time. For this setting, we explain how far the NUPBR property is affected when one stops the model by an arbitrary random time or when one incorporates fully an honest time into the model. Furthermore, we show how to construct explicitly local martingale deflator under the bigger filtration from those of the smaller filtration. As consequence, by combining the current results on the thin case and those of [3, 4], we elaborate universal results for general semimartingale models.