If it happens, because of the resources that masses of people not dying would consume, I imagine that life extension will end up being rationed; perhaps not by a totalitarian regulatory framework, but merely by being so prohibitively expensive to allow only the ultra-rich to afford it. Of course, there could be life-extension grants by governments or private foundations, allowing society's living treasures to remain living, though the politics involved in those could well result in venal, corrupt or superficially popular people winning life extension whilst politically unpopular visionaries are left to go the way of all flesh. Perhaps, ultimately, it will be automated into a reality-TV-style format, with audiences across the world getting to choose, through the internet and mobile phone voting, who gets to live forever.
Scary thought: a thousand year old Julia Robert and Hugh Grant churning out romantic film after film, decade after decade. Eventually, merely by the merit of their age will they be seen as sages, as those to ask for advice and counsel. Of course by that stage they woulod have had several "spiritual" experiences and would be well versed in righting moral wrongs.
Of course Hugh Grant might look like Yoda at that stage...
If only he talked like him, some of his films might be funnier!
Kurt Vonnegut wrote a short story /2BR02B/ ("two be or naught two be") about rationing of life: to ensure population doesn't get out of hand, every time a child is born an adult must volunteer to be executed, otherwise the child will be killed instead, because nobody dies of natural causes anymore.
Yeah. Kim Stanley Robinson touched on this during the Mars series. Where India and China ended up offloading their excess biomass on Mars. And in the long-term, people decided manned interstellar missions were actually feasible...