What happens when Oblivion Ring's enters-the-battlefield trigger and leaves-the-battlefield trigger are both on the stack at the same time?

This situation arises when a player responds to Oblivion Ring's enters-the-battlefield (ETB) trigger by finding a way to make it leave the battlefield before the ETB trigger resolves — for example, by bouncing or destroying it in response. Both triggers are now on the stack simultaneously, with the leaves-the-battlefield (LTB) trigger on top because it was put there most recently (CR 603.3, 405.6 — last-in, first-out stack order).

The LTB trigger resolves first. It says to return the exiled card to its owner's hand — but nothing has been exiled yet, so nothing is returned. The trigger does nothing (CR 603.6a — if the effect tries to do something impossible, it simply fails).

Next, the ETB trigger resolves. It exiles the chosen permanent. But now Oblivion Ring is no longer on the battlefield, so its LTB trigger will never fire again. The exiled card is gone permanently — there is no longer any mechanism to return it (CR 603.3 — a trigger only fires if the conditions are met at the time the trigger would fire).

Concrete example: Your opponent plays Oblivion Ring targeting your Gideon. In response, you cast Disenchant to destroy the Oblivion Ring. The stack is now: [ETB trigger — exile Gideon] on bottom, [LTB trigger — return exiled card] on top. The LTB trigger resolves and returns nothing. Then the ETB trigger resolves and exiles Gideon forever.

This is a well-documented interaction: the order of triggers matters enormously. The player who controls the Oblivion Ring (or an opponent causing it to die) can deliberately engineer this to exile a permanent with no possibility of return. Both triggers use the stack normally per CR 405.6 and CR 603.3.