As with many of Shakespeare's characters, there is much disagreement about the nature of Isabella's character. Is she cold and unfeeling (having "nothing" in her "alive" as you suggest) for not assisting her brother in gaining his freedom? Is her complete revulsion and disgust with Angelo's suggested alliance hypocritical, in light of her participation in deception and intrigue later in the play with Marianna? Or is she simply a female pawn in a male dominated society? It is possible to argue any one of these points of view.
These are all matters of critical opinion, and you are certainly free to form your own. Whatever assessment you make of her character, structurally, she is the main character of the play, and, as such, assists in restoring order and harmony to her world by the conclusion. At the play's end, she is pledged in marriage to the Duke and Angelo is restored to the woman to whom he has pledged himself in troth, Marianna. This resolution is meant to be seen as satisfying and harmonious, since this is the structure of Comedy as Shakespeare understood the form.
For further consideration of Isabella's character, listed in the links below are some critical assessments for you to consider in arriving at your own opinion of her nature.