We can ponder our whole lives when an zygote/embryo/fetus develops an awareness/consciousness, or when a spirit possesses it.
However, there is one thing that gives the platform for your personality, your abilities, and indeed everything that makes you more than a mere cluster of cells: cognitive ability. It can also be fair to guess that consciousness springs forth from cognitive brain functions, moreso than any other part of a human. "I think, therefor I am." It can be argued that before the fetus/embyro/whatever has developed cognitive functions, it is just an organ that is dependent on the womans body, and therefor a part of the womans body, not a separate entity.
If a person becomes braindead, "it" doesn't have the rights of a cognitive person. The rights to take medical decisision on behalf of the cognitively deceased person is passed on and those with that responsibility can pull the plug if they so decide. You could say that it is because it is impossible for the braindead person to have any further say in the matter, but I would challenge you to find someone that thinks that ending the life of that person isn't the most reasonable decision to make. The person is gone.