If Nyla leaves the battlefield before you return the card to your hand with the last ability, the card remains exiled without a way to return it to its owner's hand. If Nyla returns to the battlefield as a new object (such as if you airbend it and cast it again), it doesn't maintain connection to cards exiled by Nyla previously, and they cannot be targeted to return by the current Nyla.

Nyla, Shirshu Sleuth's second ability has an "intervening 'if' clause." That means the ability won't trigger at all unless you control no Clues at the beginning of your end step, and the ability will do nothing if you control a Clue by the time it resolves.