I am sorry you are dying without peace of mind. The answer to your question in general is yes, If somebody dies due to a doctor's malpractice, the family can sue. I have handled many wrongful death cases and in some of them, I knew the client before death and went through the dying process with the client and the family. I understand full well that it is not about money, it's about answers. I have no idea what the facts are in your case, but it might help you if you spoke to a medical malpractice lawyer now about your situation and got some expert advice. Such consultations are generally free.
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While an attorney would need significantly more information that you have provided in this question, a doctor can be sued for malpractice for failure to diagnose an illness. However, please be aware that in Tennessee the Statute of Limitations is on year. This means that you have one year from the date you knew or should have known that the doctor messed up to either settle a claim with the doctor or his insurance company or file a medical malpractice lawsuit. If you wait beyond the one year it may be to late. I hate to throw that monkey wrench into the discussion but truthfully, after your death, it may be to late. If you have information now that shows the doctor failed to diagnose, you must act now, not after your death.
I am sorry you are in such a difficult situation. The general answer to your question is yes, an action can be brought after death. However, it is important that you and your family consult a local attorney regarding the time limits for such actions. Good Luck
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