In this day and age with modern medicine, the line between life and death are blurred, as the brain dead may act as if it's alive, and the alive, due to being comatose may be reposed as if dead. What does physicalism say about this blurred line of life and death?
Physicalism says that only physical things exist and our best scientific theories are what should provide the model for that ontology. Neuroscience is our best physical theory about the brain, which is where most of our understanding of human life and death comes from, so if we believe in physicalism we should believe in what neuroscience has to tell us. You alluded to a vegetative state in your question and it should be noted that vegetation is not the same thing as brain death. I believe that the answer to this question will need some clarifications, especially about consciousness. That being said, I believe that after these clarifications it is very clear that physicalism provides a great understanding of what the line between life and death is.
Now, on to consciousness. Physicalism says that a person's mind is synonymous with their brain and that consciousness is just a collection of brain states. It's very true that we do not have an exact understanding of what consciousness is, but we do know that it is located in certain parts of the brain (the thalamus plays a central role). However, even without having the exact details down we still know (mostly) what things are involved in consciousness and (mostly) what things aren't. Organisms do not need to have a brain, or even consciousness, to be alive, though. The vast majority of life on Earth (plants, fungi, bacteria, etc.) does not have a brain.
Death of an organism is the condition wherein all biological processes that are required to sustain its life irreversibly cease to happen. Human death is defined as the complete death of all areas of the brain. This is different from any cultural idea of death as "the inability of a person to walk around, have consciousness, etc." As long as the biological processes that allow life to sustain itself are still happening, the organism is still alive. Although some people might refer to someone who is in a comatose state and does not have consciousness as being dead, our current medical understanding is that as long as they can still maintain metabolic processes unassisted they are alive. This is because, although some areas of their brain may have died, the areas that maintain the metabolic processes required to live unassisted are still functioning. Death is when all functions of the brain have irreversibly ceased.
So, imagine you have severe trauma to the brain stem, the part of the brain that controls your breathing and blood pressure (as well as some other important functions for sustaining life). Other parts of the brain, for example the frontal cortex, might not have sustained any damage from that trauma, so they might be functioning perfectly well. However, after a short amount of time, if the trauma to the brain stem was so damaging as to disallow it from functioning, then the rest of the brain will also die. If blood is not able to flow to the rest of the brain the metabolic processes of those parts will cease to happen and they will die. Cells, especially neurons, are incredibly delicate structures and if they sustain enough damage they will never be able to function again. If enough of these cells are damaged then the brain will never be able to function again. This is why death is irreversible. In this case of the death of the brain stem, the person may still be conscious for a few moments afterwards. The parts of the brain that control consciousness have not yet suffered cell death and are continuing to function. However, once the lack of blood causes those cells to die as well all areas of the brain will have ceased to function and the person will be dead.
The exact point of death is best understood as the point where cell death has become so great that any sort of ability to reverse the processes is gone. Now, it’s true that we put a lot focus on the brain because the brain is what normally regulates our entire body. The brain is what controls our respiratory and circulatory systems and without the brain those systems will fail. For humans being in a state where those systems fail and damage is caused that will reversibly forbid them to ever function on their own again is synonymous with dying. The person could have been without consciousness due to other trauma to the brain for months before that moment. In that situation, as long as their brain stem still functioned and they were able to live unassisted they would still be alive. However, the moment that the rest of the brain loses its ability to function, the person will die.