This paper quantifies the impact of stopping at a random time on non-arbitrage, for a class of semimartingale models. We focus on No-Unbounded-Profit-with-Bounded-Risk (called NUPBR hereafter) concept, also known in the literature as the arbitrage of the first kind. The first principal result lies in describing the pairs of market model and random times for which the resulting stopped model fulfills the NUPBR condition. The second principal result characterises the random time models that preserve the NUPBR property after stopping for any quasi-left-continuous market model. The analysis that drives these results is based on new stochastic developments in martingale theory with progressive enlargement of filtration. Furthermore, we construct explicit martingale densities (deflators) for a subclass of local martingales when stopped at a random time.