Assuming of course they are not in a persistant long term vegetative state.
The question is where we draw the line. And again, the answer is not an easy one.
IANAD, but my understanding is that while many bodily systems can run for awhile on "autopilot" without needing any control feedback from the brain, things generally go out of kilter pretty quickly and severely when the brain is non-functional. To use a crude analogy, a factory full of automated equipment might not need constant human intervention to manufacture product beyond keeping supply hoppers filled and finished-product areas clear, but if left unattended for too long the equipment will drift out of spec and eventually start malfunctioning and even self-destruct.
BTW, this case has an interesting twist compared with Terri's: here, the person widely suspected of causing the incapacitated person's injuries has a vested interest in her recovery. Even if the girl were to recover sufficiently to testify against her assailants, such recovery would guarantee that they could at worst be charged with attempted murder. And if they could convince a jury that they were instrumental in assisting the girl's recovery, they could likely win some jury sympathy and get prosecuted of something even less.
I agree with you that we can take a person off the respirator after a while, i.e., after we've tried to help them breathe. But taking away food and water will kill even the healthiest person.
Everyone should be given food and water. Then, if they die, it will be because God allowed it, NOT because we killed them.