“He who dies with the most toys wins,” read the '80s bumper sticker. What about he who dies with nothing at all? 

It happens every day. One in five of the oldest retirees is dying with no assets except a home, according to a new study by the Employee Benefit Research Institute, or EBRI. And almost a quarter of those 85 and older are dying with less than $10,000, including the value of their homes. 

To be old and running out of money is a scary fate, and it’s one that more Americans face. Nowadays, a 65-year-old man in the U.S. can expect to live to 84, while the life expectancy for a 65-year-old woman is 87. The Center for Retirement Research estimates that 52 percent of working-age adults were “at risk” in 2013 of not having enough when they retire. That’s up from 43 percent in 2004. 

Americans are given the same retirement advice over and over: Save more. Work longer. But it’s rarely that simple. Health problems and age discrimination can make it impossible to work as long as you want. And stagnant wages and everyday life make it tough to save the 15 percent of household income that the Center for Retirement Research suggests.

Even substantial wealth is no guarantee you won’t burn through your fortune well before you die. A private room in a typical nursing home costs $91,250 this year, according to Genworth estimates released this month. And it's far more in expensive areas. At $158,775 a year, a Connecticut retiree with Alzheimer’s disease could burn through $1 million in a little more than six years.

It's true, richer retirees have options to preserve their fortunes for life. They can afford to buy insurance. Long-term care insurance can pay for nursing homes or home health care. Longevity annuities can provide monthly payments in old age, and those checks are bigger than in regular annuities because they start paying only if you’re lucky enough to reach the age of 80 or 85. 

Many middle- and working-class people, meanwhile, no longer have the defined-benefit pension that makes saving automatic and provides a guaranteed income stream for life. When faced with long-term care expenses, their best strategy is often to burn through their assets and qualify for Medicaid, the government health program for the poor.

But there's a cruel irony at work here, for rich and poor and everyone in between. Wealthier people, many of whom have been able to save substantial amounts, tend to be healthier and to live longer than poorer Americans. Because many people who die young are poor, they’re likelier to die penniless. But, the EBRI study shows, people who are well off still risk dying poor, especially by the time they are 85. 

One thing that makes it tricky to avoid running out of money: You have no idea how long you’ll live. It’s easy to be wrong by a decade or more. Spend too much of your nest egg, and you might end up a destitute 93-year-old. Spend too little and die young, and you missed the chance to enjoy your savings. 

The Center for Retirement Research just released some recommendations, for both retirees and policy makers, to stave off “the coming retirement crisis.” Social Security should get more revenue, the Center says, and saving for 401(k) retirement plans should be automatic for all workers. Americans should work longer, to age 70 whenever possible, and more homewners should consider tapping the equity in their homes to pay for their daily expenses.