When it comes to human beings, it is very difficult to define the living state. A person may lie in coma for several years. By technical definition, the person is alive because he is not brain-dead. However, most of his vital organs have stopped functioning. Such a person is kept alive with life support system. A heart and lung machine works continuously to perform the function of oxygenation and circulation. A dialysis unit may be in place to perform the function of kidneys. The person gets nutrition through intravenous fluids. Since the person is in comma so he is not exhibiting consciousness to his environment. In other words, he is not exhibiting response to stimuli; which is one of the defining criteria for life.
Since the person is being kept alive because of life support system; metabolic activities are going on. Hence, the person can be considered as dead. 

But we should not forget that once he is put off the life support system; he will become brain-dead immediately and will be dead by technical definition. 
So, this is a difficult question whether a person in comma is dead or alive.