Henry Fool and the Schroedinger’s Ending
So over in this comment thread we were talking about branching story and choose-your-own-adventure and how much I hate them. But I thought of an instance where I didn’t mind the audience getting to choose an outcome. A story with a seemingly ambiguous ending, but where the possible outcomes are really very few, and those options are clearly defined, allowing you as the audience to choose which one you believe happened. In this case, all of these endings exist simultaneously, all are valid, all have been clearly articulated by they author, and if I choose to believe one ending it has no effect on your ability to believe the other one.
The first example that sprang to mind was Henry running on the tarmac at the end of Henry Fool.
(This assumes you ignore the existence of the sequel Fay Grim, which I’ve only seen once and disliked, mainly for ruining the Schroedinger’s Ending of it’s antecedent.)