They can, but it is wrong.
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Your question does not make it clear whether the "burning" of your fallopian tubes was something done as part of the overall procedure to remove fibroids, particularly because of fibroids that someway involved the tubes, or were you told that it was an unintentional event that occured while they were removing the fibroids. This is very important to trying to determine if malpractice was committed. When you were told of this circumstance, were you advised how bad the "burn" injury was, and the possible long term affects therefrom. This is important for you to try to determine if the injury is serious enough to warrant the time and expense of a lawsuit. Aside from that, and under any circumstance, the doctor was required to inform you of all possible risks of the surgery you were going to have, in order to allow you to give considered and thoughtful consent as to whether to go through with the procedure. This is called "informed consent". The failure to give, or obtain, informed consent is a grounds for liability even if what happened to you was not the result of malpractice.