The falling action of the story is actually the point at which the princess waves her hand to the right and the story ends. There is no resolution, the ending is ambiguous, meaning you choose what you think happened at the end.
Something interesting about this ambiguous ending is that Stockton never knew that it would draw the attention that it did. He had angry readers demanding that he write an ending to the story. When he finally came forward with an answer to everyone's burning question, "the lady or the tiger?" his answer was that whichever door the reader believed the princess pointed to could be revealing about the reader's character. That's it- he never wrote an ending. It makes the story really great for thought because you really sit back and think about what you yourself might do and why and what that says about your own character.
This famous and provocative short story takes the reader to the point where the climax should occur, the point when the reader learns which door the young man chooses and what his fate is, but the author does not provide a climax. Instead, he leaves us questioning which came out of the door, the lady or the tiger. Without a climax, the story therefore has no falling action or resolution.