I believe that the lady came out of the door the young man opened.
Explanation:
"The Lady, or The Tiger" is a short story by 'Frank Richard Stockton'. The author has not ended the story with a certain answer telling the fate of the young man who dared to love the king's daughter.
The young man would have opened the door which lady behind it, as directed by the princess because both loved each other intensely. The mere thought of man being eaten by the tiger affected the princess immensely. She loved him a lot and there was no one in the courtier who had dared to love the royal princess ever before.
So, princess would not have hurt the young man and let him marry someone else.
