Spoilers, obviously.
In the story quest, you can choose to hand over your own Hibernation Chamber key or not in order to prove to the other sibling that you, the player met Direidyth should they reach her (well, they didn't, and she turned into a Hilichurl over time anyways).
But if you're not doing that, then Direidyth will receive the Hibernation Chamber key from your other sibling after meeting them and said that she met someone like them. It is presumed that your sibling went out, searching for the player and left the key to Direidyth in hopes that you came back to the spot.
Either way, both of you will not return to the cave until sometime has passed, and thus nobody saved Direidyth from becoming a Hilichurl, waiting for either of the siblings to come back. This will start the stable time loop of which you gotten yourself the Hibernation Chamber key in the first place and enter the time anomaly, thus progressing the events.