In November 2007, the 14th Dalai Lama suggested he might not be reborn, or else he might choose the next Dalai Lama while he is still alive. That really would not be completely unheard of, since in Buddhism linear time is considered a delusion, and since rebirth is not really of one individual. I understand there have been other circumstances in which a new high lama was born before the former one died.
His Holiness is concerned that the Chinese will choose and install the 15th Dalai Lama, as they have done with the Panchen Lama. The Panchen Lama is the second-highest spiritual leader of Tibet.
On May 14, 1995, the Dalai Lama identified a six-year-old boy named Gedhun Choekyi Nyima as the 11th reincarnation of the Panchen Lama. By May 17 the boy and his parents had been taken into Chinese custody. They have not been seen or heard from since. The Chinese government named another boy, Gyaltsen Norbu, as the official 11th Panchen Lama and had him enthroned in November 1995. See also “The Tragedy of the Panchen Lama.”
No decisions have been made at this time, I don’t believe. But given the situation in Tibet, it is entirely possible the institution of Dalai Lama will come to an end when the 14th Dalai Lama dies.