All items produced or collected as part of the ongoing event become irrelevant after its end and automatically disappear from the storage. You are only left with the prize items and chests obtained in the Magic Store. You may store these chests and open them even after the event ends.
Please note, that the chests appearance may be altered from one event to another: if you collected Dream Shards in the “Dreams of Time”, then these items may look differently in the forthcoming events (e.g., Dream Shards may be transformed into Trunks from “The Headless Horseman”), but they will still have the same contents.
Also note, that the chests obtained in an event are not counted in any other event’s quests.