That has already happened. Any financial cushion that was there has been exhausted. My wife had heart attack three years ago. We are both out of work and the only insurance in place was Cobra. In our situation Cobra didn't cover that much so most of our "savings for future" are gone.
With today's economy and employment situation I'm sure it is going to get a lot worse before it gets better. More and more people are loosing assets each day. Those approaching senior years that have no fear are fools. Costs keep rising and as duffsmom says assets/savings cannot grow at the same pace.
Sooner or later you get hit with the fact that a dollar saved is not worth that same dollar in real life when you retire. Outliving your money and assets is a real situation that few people think about or plan for. And I'm not sure with the way things are going one can plan well enough to be completely safe.