SAN FRANCISCO (MarketWatch)—Almost half of U.S. retirees die with savings of $10,000 or less, but that grim finding doesn’t fully describe the variability and uncertainty that characterize retirement in America, according to a recent study.

While some retirees struggle profoundly, living at or below the poverty line, others enjoy wealth and health—in fact, the two are strongly linked—while still others have little in savings but enjoy a decent income, according to the report, based on a survey that tracked retirees from 1993 through 2008.

While 46% of retirees have just $10,000 in savings when they die, “That doesn’t mean their standard of living is very low—they might have a relatively generous pension plan, most of them will have Social Security,” said James Poterba, professor of economics at M.I.T., president of the National Bureau of Economic Research, and a co-author of the study.

But the findings “suggest something about the financial resiliency of these households,” Poterba added. “They may not have much capacity to absorb a shock, such as an out-of-pocket medical expenditure. They don’t have very much in the way of liquid assets they can access.” Read the study here.

When net worth is measured—including savings, home equity, the value of Social Security and pension benefits, and more—retirees’ financial picture around the time of death looks less bleak. Single people had average assets of about $142,000, those whose spouse had died previously had average assets of $253,000, and couples where the surveyed retiree had died but the other spouse was still living had average assets of $692,000, according to the study.

“You can’t generalize that the elderly are not doing very well financially or that the elderly are doing fine. There is a lot of variation within the group,” Poterba said. “There is a clear group of households that have relatively low income and also have low financial assets. At the other end is a group that has financial assets that are more than sufficient to accommodate any shocks.”

Policy makers and financial advisers, take note. “One-size-fits-all solutions are unlikely to really capture the flavor of what’s here,” Poterba said.

Incomes in flux

Another worrisome finding: The degree to which some retirees face a steep drop in income. While single people and married couples saw their retirement income remain fairly steady, on average, that was not the case for retirees whose spouse had died.

Their income dropped almost 75% between 1993 and the last year of being surveyed. The study doesn’t explain why that happens, though Poterba hazarded a guess that it might be related to a drop in pension benefits when the first spouse dies.

Get married

If you want the best retirement outcome possible, get rich. If that fails, consider getting married, staying married—and doing your best to die before your spouse does. That last is not entirely serious, but the general take-away is that being married pays off in retirement.

For example, remember that 46% of retirees who have just $10,000 in savings when they die? That jumps to 57% for people who are single throughout the course of the survey.

Married couples are likelier to have home equity, too. Overall, in the last year before death, 57% of single-person households and 50% of surviving spouses had no housing wealth when they died. But retirees who died before their spouse did? Just 20% lacked home equity, the study said.

“The group who does the best in terms of average level of financial assets are those who are married when we first see them, remain married when the first person dies, and we’re looking at the first spouse to die. They tend to have higher income levels,” Poterba said. “Single individuals on average have lower levels of retirement income as well as lower financial assets.”

But perhaps the study’s most striking finding was a “strong and consistent” relationship between wealth and survival. If you’re rich, you’re much likelier to live longer.

“The relationship between wealth when first observed and subsequent mortality is striking,” the study said.