Despite the discovery of thousands of transiting planets orbiting main sequence stars, the population of planets around red giant stars remains poorly understood. Recent studies have shown that comparisons between this planet population and analogous main sequence systems can reveal effects of stellar evolution and orbital dynamics on the inflation of planetary atmospheres, as well as planet orbital evolution and eventual engulfment. The current NASA TESS mission is rapidly expanding our ability to detect planets transiting evolved stars and better understand this uniquely valuable planet population. I will present the most recent planet discoveries around evolved stars from TESS, and place these systems in the context of the larger planet population to highlight the new constraints these systems provide on our understanding of planetary orbital evolution. Specifically, I will focus on the planets found with the shortest orbital periods, and how their TESS light curves provide new constraints on models of star and planet tidal evolution and interaction. Finally, I will discuss the future followup of other planetary candidates around evolved stars from TESS, and describe the potential of future missions such as JWST to characterize the atmospheres and compositions of these dying planets.