The simple answer is yes, but patients and their families need to understand why, so that they can make well informed decisions regarding Surgical intervention. Serious Trauma patients often enter Surgery with little chance of survival, but if they die on the OR table from catastrophic injuries the Surgeon is rarely to blame. Would close family members not want the Surgeon to even attempt to take extraordinary measures to save a life? The risk of a complication from anesthesia is rare, but not necessarily due to any error. In the majority of cases where a patient dies during Surgery no one is to blame and reasonable people should not seek to punish those whose job of work is to save lives if at all possible.
There are always certain risks associated with Surgery, but this must be fully explained to the patient prior to their operation when they are asked to sign a Consent Form. This is referred to as giving "informed consent" by acknowledging that you understand all of the potential risks or complications that might occur during or as a direct consequence of Surgery. Everything that we decide to do to treat a patient, including Surgery, comes down to Risk/Benefit: does the potential benefit to the patient outweigh the risk involved? On certain occasions extremely skilled Surgeons will attempt a case that has very little chance of success, but if the patient's prognosis for survival without Surgery is dismal anyway, this too may be worth the risk. While no Surgery is completely risk free the patient is asked to decide whether that risk is acceptable under the circumstances and all circumstances are different.
The patient or family member signing consent for Surgery must also bear some responsibility for the outcome as complications can also be due to incorrect information supplied to the Surgical team by the patient or the patient's non-compliance with important instructions and therefore not related to any error made by the team. Due to the propensity for legal action nowadays, a Surgeon is more likely to err on the side of presenting the worst case scenario to their patient to discourage unreasonable expectations. Sadly, this can also diminish a patient's will to live and their determination to survive a complicated Surgery! Patients must try to remain positive and proactive in their own care plan. It is absolutely vital to make sure that you fully understand the risks of Surgery before signing a consent form and do not be afraid to ask questions of the Surgical team prior to signing: if you do not anticipate risk you have not made an informed decision.