Fractured or broken instruments usually occur after RCT.  The dentist uses a reamer or a small file to shape the root and in doing so normally does not notice that part of the reamer or file has broken off.  Whilst is it not negligent to fracture an instrument whilst carrying out RCT, it IS negligent  not to diagnose and treat the fracture and also negligent not to tell the patient that a fractured instrument has occurred.