How Kate could stay alive?

they've done a lot of ghosts on NCIS.

not as supernatural spirits but in dreams, delirious visions and flashback memories

gibbs has even had conversations with dead people (he was shot and dieing at the time)

it works as long as it isn't presented as anything other than a dream or a delusion

She was hit in the front of the skull by a bullet that penetrated deep into her head, tearing apart delicate brain tissue along the way. Her colleagues examined her closely and determined that she was not only merely dead, she was really most sincerely dead.