Sure, the name of the plaintiff can change to The Estate of X.  Your medical malpractice attorney should be aware of this.  Also, if the person died due to the medical malpractice that was the subject of the lawsuit, often times the medical malpractice suit becomes a suit for wrongful death, and the relatives become the plaintiffs.  In Arizona, the parents, children and spouse of the deceased have a right to sue for wrongful death.  Again, your medical malpractice attorney should be able to covert the lawsuit after death to whatever is appropriate in your state.