The games research community has developed substantial knowledge on designing engaging experiences that draw players in. Surprisingly, less is known about player \textit{dis}engagement, with existing work predominantly addressing disengagement from the perspective of problematic play, and research exploring player disengagement from a constructive designer perspective is lacking. In this paper, we address this gap and argue that disengagement from games should be constructively designed, allowing players to exit play sessions in a self-determined way. Following a two-phase research approach that combines an interview study (n=16) with a follow-up online survey (n=111), we systematically analyze player perspectives on exiting play sessions. Our work expands the existing notion of disengagement through a characterization of exit experiences, a lens on disengagement as a process, and points for reflection for the design of games that seek to address player disengagement in a constructive way.