Each event is different and the prizes are distributed differently. Most events will require players to claim the reward and must be claimed within the claiming period for the event. If that period has expired, the reward will be forfeited.
Distribution of rewards varies with some distributed automatically while others will be sent to the game's inbox and players will need to claim them manually. If you're rewarded with a timed reward, those will become effective as soon as you claim it, meaning the timer will countdown immediately. If players do not use it right away, then it cannot be recovered.