Had Desdemona not died, how do you feel Shakespeare's Othello would have ended?
This is almost a trick question. Desdemona dies at Othello's hand, smothered by her own husband and in her own bedchamber. Does Desdemona's continued life mean that Othello decided not to try and kill her, despite her suspected guilt? Does Desdemona's continued life mean that Othello FAILED in his attempt? Does Desdemona's continued life mean that she was resurrected by Othello's kiss before HE dies at the end? Does Desdemona's continued life change the story so much that Othello learns the truth about his wife's fidelity therefore negating his jealousy? Does Desdemona's continued life mean that Othello ALSO would not have died (through stabbing himself) at the end of the play? As you can see, there are just so many factors that could exacerbate the situation, that the continued life of Desdemona is almost impossible to imagine. This is actually a testament to Shakespeare's craft in writing this play. Our William Shakespeare has set the tragedy up so very perfectly.
Therefore, in order to answer your question, I am going to pretend to forget about the "how" in regard to these possibilities, and simply answer as if I haven't thought about them.
Quite simply, "had Desdemona not died," then Othello would have begged her forgiveness for his misplaced (and violent) jealousy, renewed his vows, and the couple would have begun their life anew. This is a testament to how beautiful and true Desdemona is. An understanding woman and wife, she would see the evils of Iago in their true light and how it was THOSE evils that led her husband into the errors of jealousy. Love is a powerful force. Love inspires forgiveness. (Further, Othello's pre-death kiss at the end of the play shows his love and his remorse and his wish for things to be different.) Let's look at that moment in the play so as to cement the emotions in our minds:
Then must you speak
Of one that loved not wisely but too well;
Of one not easily jealous, but, being wrought,
Perplex'd in the extreme; of one whose hand,(395)
Like the base Indian, threw a pearl away
Richer than all his tribe ...
Stabs Himself ...
I kissed thee ere I kill'd thee.
No way but this,
Killing myself, to die upon a kiss.
In conclusion, I believe that Othello has spoken truth here. Although he has been marred by jealousy due to the true evil genius of Iago, he is right in saying that he has "loved ... too well." He admits his love, even now. If Desdemona had not died, their love would continue. Nothing, before this, could thwart Desdemona's love for Othello. Why would the knowledge of his jealous mistakes? In short, Desdemona's continued life would turn this tragedy into a comedy. Truly! There would be a happy married couple and, further, only the people condemned by their own evil plot would suffer death. As it stands now, however, the ending should remind us of the deaths of Juliet and Romeo.