Livestreaming has evolved into a thriving industry where creators can directly monetize and engage with their audiences and followers. In practice, creators and platforms typically concentrate their marketing efforts on the period leading up to the livestream. However, livestreaming events naturally transition into recorded formats once the event concludes, creating potential "residual" opportunities for monetization. This study systematically examines consumer demand for live events throughout the entire livestream life-cycle, using data from a large livestreaming platform that allows consumers to purchase the recorded version of a paid live event after the livestream ends. We find that the demand is surprisingly more price-sensitive during the pre-livestream period compared to the post-period. This is partly driven by two mechanisms: consumer self-selection (infrequent consumers who may have missed the live events exhibit a higher willingness to pay for recorded versions) and quality uncertainty (consumers face higher uncertainty in event quality during the pre-period than in the post-period). Our findings generate implications for the pricing and targeting strategies in livestreaming markets.