I think its pretty clear that your consciousness is linked to the health of your brain. How else do you explain the effects of Alzheimer's, brain damage or other brain diseases? So its logical to believe that brain death or destruction is also the death of your consciousness.
Note: the death of consciousness doesn't preclude the possibility of an afterlife, as I think Christians believe in a bodily resurrection -- that is they were completely dead, but are reborn with perfect bodies via divine intervention or miracle, same as Jesus. Its probably similar in other religions too. This probably does put the kybosh on people coming back as ghosts and other silliness though.
Note: the death of consciousness doesn't preclude the possibility of an afterlife, as I think Christians believe in a bodily resurrection -- that is they were completely dead, but are reborn with perfect bodies via divine intervention or miracle, same as Jesus. Its probably similar in other religions too. This probably does put the kybosh on people coming back as ghosts and other silliness though.