Obtaining consent for organ donation from a competent ICU patient who does not want to live anymore and who is dependent on life-sustaining treatment; ethically feasible?

We anticipate a further decline of patients who eventually will become brain dead. The intensive care unit (ICU) is considered a last resort for patients with severe and multiple organ dysfunction. Patients with primary central nervous system failure constitute the largest group of patients in which life-sustaining treatment is withdrawn. Almost all these patients are unconscious at the moment physicians decide to withhold and withdraw life-sustaining measures. Sometimes, however competent ICU patients state that they do not want to live anymore because of the severity of their illness or the poor prognosis and ask for withdrawal of life-sustaining measures like mechanical ventilation. Do we consider the unconscious patient as potential organ donor before withdrawal of mechanical ventilation? This is paradoxically rare in the case of the conscious ICU patient. Is it practically possible and ethically feasible to obtain consent for organ donation from this group of patients?