A nameless narrator goes to Venice to find Juliana Bordereau, an old lover of Jeffrey Aspern, a famous and now dead American poet. The narrator presents himself to the old woman as a prospective lodger and is prepared to court her niece Miss Tita (renamed Miss Tina in later editions), a plain, somewhat naive spinster, in hopes of getting a look at some of Aspern's letters and other papers kept by Juliana. Miss Tita had denied the existence of any such papers in a letter to the narrator and his publishing partner, but he believes she was dissembling on instructions from Juliana. The narrator eventually discloses his intentions to Miss Tita, who promises to help him.
Later, Juliana offers to sell a portrait miniature of Aspern to the narrator for an exorbitant price. She doesn't mention Jeffrey Aspern's name, but the narrator still believes she possesses some of his letters. When the old woman falls ill, the narrator ventures into her room and gets caught by Juliana as he is about to rifle her desk for the letters. Juliana calls the narrator a "publishing scoundrel" and collapses. The narrator flees, and when he returns some days later, he discovers that Juliana has died. Miss Tita hints that he can have the Aspern letters if he marries her.
Again, the narrator flees. At first he feels he can never accept the proposal, but gradually he begins to change his mind. When he returns to see Miss Tita, she bids him farewell and tells him that she has burned all the letters one by one. The narrator never sees the precious papers, but he does send Miss Tita some money for the miniature portrait of Aspern that she gives him.

Question: Does the main character come away from the situation with anything regarding the poet?
Answer: He has the portrait and pays Miss Tita for that.
Alternative answer: No