Emergent property is defined as an organ, which is more important than its parts. So like cell -> tissue -> organs -> organ system -> organism. So I guess that if a patient is about to be removed from the life supporting apparatus, the doctor must be sure that the patient is going to die even if the apparatus was on. So for the doctor to make sure that the patient is going to die for sure, he needs to check on his heart and brains and other vital organs that will continue his/her life.
In my personal opinion, if the dying patient is surely about to die within a certain amount of time, I believe that the doctor can remove the apparatus. Some people might say that it is immoral to do that, but until when will they waste the apparatus on dying person, when the apparatus can be used to other patients who have higher chances of living. But in most cases it might depend on the family members and the choice of the patient.