In situ and orbital observations have suggested that Jezero crater (field site for the Mars 2020 Perseverance rover) once hosted a paleolake fed by two inlet valleys. An outlet valley, Pliva Vallis, is present on the eastern rim of the crater and raises the question of whether the lake system operated as an open basin or as a closed basin system with one or more overflow events. To tackle this uncertainty, we present a detailed morphological study of Pliva Vallis, using digital elevation models and imagery. The atypical morphology of the valley, including reincised fluvial layered deposits, a perched valley, and bedrock incision terraces, led us to interpret that Pliva Vallis was formed by discontinuous and episodic flows rather than from a steady outlet river. These observations allowed us to infer at least four main breach episodes and propose a new scenario for the evolution of the lake system over time. We give a minimum estimate of the duration of these overflow events using a 0-D model, simulating a valley formation by breach erosion and lake overflow. Modeling results suggest that each flood event causing a part of the incision of the outlet valley would not have lasted for more than a few weeks, and some may have lasted only a few days. These time scales are consistent with our morphological interpretation that the outlet valley was carved by discontinuous and temporary flows. In this scenario, Jezero lake was predominantly a closed basin, spilling over episodically in at least four breach events.