When the dead are not allowed to die

In the United States the case of the 13-year-old Jahi McMath has regularly been making the headlines since December. The girl had had her tonsils removed surgically, but after the procedure she went into cardiac arrest and was declared brain dead shortly afterwards. Her family didn't accept her passing and wanted her to be kept on life support, while the hospital and the coroner wanted her to be taken off the ventilator, so they could start their investigation on Jahi's death.
The family moved to court, insisting the girl showed signs of life, but the judge declared her brain dead, too. Now - with the coroner's consent, since she's legally dead - the girl's body, attached to a ventilator, has been released from the hospital and transferred to an undisclosed facility while Jahi's family keeps on hoping for her recovery.

I of course understand the tragedy of the situation, the grief of the family and that they are hoping beyond reason that their little girl might recover, but the sad fact is that she's dead. Her brain has stopped working and even if they keep her on life support for the next twenty years that's not going to change, unless a true miracle happens. By prolonging her body's "life" they are just prolonging their own suffering.

If they let her die peacefully instead of clinging on to an irrational hope, they could start grieving and, over time, come to terms with their fate. Maybe this would also be in Jahi's best interest.
If I were to fall into a coma or be declared brain dead, I would want to be taken off life support as soon as possible. To me, the idea of being in a completely helpless state, only kept alive by machines, is utterly humiliating. I'm aware that probably nobody of my friends and family would want to make this decision, but if the doctors tell you that it's unlikely that I'm ever going to be my old self again, then please pull the plug on me. I do not wish to be, under any circumstances, some helpless, motionless, lifeless being that is nothing more than the focus of pity, grief, and sadness.