[Kalimac]

Maybe she was going to die. In fact, I would bet on that in the absence of anything else. She's certainly set up for it; unhappy, caged, wanting only to break free and prove herself, so to speak. Even in the books as they are now Eowyn is pretty much longing for death for a good part of it - in the Houses of Healing, before she meets Faramir, her mind continues to be worsening even though her body is on the mend, and she is angry that she will not have another chance to die in battle.

It would be a powerful ending for her - she breaks free of her cage by the most desperate measure possible, and by heroically sacrificing her life to kill the Witch-King and save her people. If that was the case, it's just as well that Faramir came along when he did; as dramatic as that story would have been, far more comfortable for Eowyn personally to end up with a date with Faramir instead of the Grim Reaper.