Hearing that your relative has died while in surgery or due to a medical emergency is devastating enough without also hearing that it may have been preventable. Medical mistakes and negligence are unfortunately a lot more common than they should be, and if your family member was the victim of negligence, for example, then you need to take action. But it is also possible for these medical events and deaths to be due to confusion from an unknown condition or a situation that couldn't be helped. It's essential to know the difference between doctors trying their best and not succeeding, and doctors not really trying at all.
One of the keys to determining whether an action (or lack thereof) was negligent is whether the knowledge driving the action was something the doctors and other medical professionals could have reasonably known. Doctors are expected to know that not all headaches are just headaches, for example; if someone presents with certain qualifying symptoms, that patient needs further testing to rule out conditions like tumors or aneurysms.
Let's say the patient showed signs of an aneurysm, underwent tests to diagnose one, and was told they were fine because there were no signs of an aneurysm in the results -- only to later die from an aneurysm because the signs were actually well-hidden. That might be an unfortunate event. The doctors did try to diagnose the condition and were given results that were consistent with the patient being just fine.
Now let's say that the patient presented with those qualifying symptoms only to be told by the doctor that he or she (the patient) was much too young to have anything other than a headache. The patient died from an undiagnosed aneurysm, and an autopsy showed that tests would have diagnosed the condition easily.
In that case, you could be looking at a massive wrongful death suit because the doctor could have been reasonably expected to order tests based on symptoms.
Another issue is that sometimes there are unavoidable effects from some treatments that could interfere with other treatments. A patient who fights doctors trying to save him may need to be sedated -- but if it turns out the sedative lowers his blood pressure and makes it harder for him to recover, that's not really the doctors' fault. They had to do something to get him to stop fighting so they could do their jobs, after all.
At the same time, if the doctors sedated a calm patient just in case while knowing full well that the sedative's side effects could be fatal, then you've got a probably wrongful death case.
Those two examples are fairly extreme; in many cases, telling the difference is a lot harder. You need to talk to a lawyer at firms like Shay & Associates who specializes in wrongful death cases to help determine if the doctors did not do their jobs properly.