Solid State

People noticed almost immediately.
The world's attention was caught when all those with deadly diseases suddenly didn't have them any longer. Everyone proclaimed it a miracle. Celebrations were held all over the world, and an international day of peace was declared.
At first, they didn't notice that anything else wrong. There was the occasional odd report of a failed suicide, or some 'nutjob' claiming they couldn't die, but for the most part, everyone ignored it.

Then came the jump.

A man tried to suicide off the top of the new World Trade Center. He hit the ground, breaking nearly every bone in his body, and turning nearly every organ to mush. But he was still alive. He healed at an incredibly fast rate, and within a month, it was as if nothing had happened to him at all. Suddenly, reports came pouring in of people who couldn't die. And of those who could. Everyone from around the age of thirty up could die. The rest... well, those reports did not make for light reading.
The rest of the effects took longer to ascertain. It was an entire year before everyone realized that no more babies were being born. Nobody could have children. And several more years passed before it became apparent that nobody below thirty was aging beyond the appearance of youth. Everyone above thirty kept getting older. The population of the earth, for the first time in thousands of years, began to shrink. Some began to panic. Doctors all over the world met together, trying to find a 'cure', though there didn't seem to be any physical reason for the sudden, global change. It was as if time had simply stopped for the younger generation.
Over the next forty years, the population of the earth slowly dwindled, until only a few elders were left, and there were no young children.
By this time, everyone had begun to realize something.

They had all the time in the world...