Is the Dalai lama an institution? Or is he the man who is the 14th Dalai Lama? So let's begin with the Dalai Lama as an institution. As HH Dalai Lama says, the institution of the Dalai Lama can fade away. Just like the Buddha is not an institution, neither is the Dalai Lama. What is more important are the teachings. The Buddha's teachings have endured to this day. So too will the Dalai Lama's books and teachings of the Dharma endure.
HH Dalai Lama was chosen as a successor to the 13th Dalai Lama following strict guidelines that had existed for a long time. HH Dalai Lama was already 'discovere', as the successor when he was only two years old. He fitted the god-king image that tradition-bound Tibetans had of their Dalai Lama. Furthermore, the charisma of the current Dalai Lama has lent much aura to this image. However, if He were to pass on, the traditional method would be made a mockery of by the Chinese. They would choose their own successor and proclaim him as the legitimate successor. However closely the Tibetans follow the traditional process of ascertaining the successor, the Chinese would impose their own selected Dalai Lama on the Tibetans. When that happens, will there be two Dalai Lamas, one Chinese-appointed one within Tibet(in China) and one outside Tibet - in India?
Then again, if we look hard at the Tibetans of today, there are now two groups- one group still in Tibet and the other group is made up of the diaspora outside Tibet.For the ones in Tibet, Tibetan culture and tradition regarding the Dalai Lama as a God-king, would by now have no strong hold on their minds. By now, there would be a much reduced number of Tibetans within Tibet seeing the Dalai Lama as the god-king, as those, who had wanted to see HH Dalai Lama free Tibet, have been deeply disappointed in Him. The diaspora outside Tibet are mostly bent on pursuing the comfortable life that the Western countries seem to offer them than to continue maintaining devotion to a god-king in exile.
Thus by these counts, it is unlikely that there will be much interest in a successor to the Dalai Lama, especially now that he has given up His political role. Also, people today, including the Tibetans-in-exile, are not so concerned about someone who had held sway in Tibet(as both spiritual and temporal head), before the Chinese invasion.