These people fear the bill collector more than the Grim Reaper.
Among workers ages 40 and 50, nearly half fear the financial consequences of a critical illness—compared with just 29 percent who rate dying as their biggest concern, according to a new study.
That fear of a hit to the wallet being a bigger concern than dying is most pronounced among single workers, single women and single parents, according to the Sun Life Financial survey, "Well-Placed Fears: Workers' Perceptions of a Critical Illness."
For example, single women in that 40-50 age group who earn less than $50,000 are four times more concerned about the financial fallout of a critical illness than they are worried about being killed by it, the report found.
(Read more: For millions of workers, getting sick doesn't pay)
And most single parents and single women ages 22 to 39 in that income bracket are more worried about paying the bills from those illnesses than dying from them.
Despite those stark money-related fears, the overwhelming majority of American workers are going without insurance coverage that would specifically pay bills from a critical illness.
Thirty-six percent of the workers who responded to the survey believe they have critical illness coverage—but less than 5 percent of all workers are estimated to actually carry such coverage.
"Our findings suggest that benefits brokers and [human resources] decision-makers might especially want to consider offering critical illness and cancer insurance if their employee base contains a significant group of women, workers age 40 to 50 or singles," said Bob Klein, senior vice president of Sun Life's voluntary and multi-line divisions.
Klein's singling out of cancer stemmed from another major finding of the survey, which polled more than 4,100 full-time workers and was conducted by Kelton Research.
Nearly half of all workers polled—48 percent—were most worried about falling victim to an invasive cancer. Heart attack was the top concern for 32 percent, and stroke for 15 percent.
Ironically, those diseases' costs are inversely related to the degree that people worry about them. Stroke has an out-of-pocket average cost of $17,680, followed by heart attack with an average cost of $14,234, and cancer at $6,740, Sun Life Financial noted.
The study not only found that people were worried about the financial effect of a critical illness; they had actually felt such effects after falling victim.
Of the 285 survey respondents who had suffered a critical illness, two-thirds had to take special measures to cover related costs. A total of 28 percent tapped their retirement savings and other funds earmarked for future needs, 28 percent dipped into emergency funds and 21 percent borrowed money from family or friends. Twelve percent declared bankruptcy and 11 percent either sold their homes or had them foreclosed upon.
Klein said that the research "underscores that even if you have robust health coverage, a significant health condition such as cancer, heart attack or stroke can divert a significant chunk of money from your savings, or, in some cases, cost you your home."
Klein also said that based on the study's results, "we think many workers will want to explore ways to increase their financial security in case they experience a critical illness."
John Hauserman, a certified financial planner, said his clients are "very fearful" of a critical illness putting a big dent in their wallets and putting them out of work for a long time.
"Once you're having that conversation, you can see the alarm bells going off, but people don't come in asking about it," said Hauserman. "Consistently, probably 90 percent of the time, I'm the one who brings that up."
Hauserman said he views critical illness insurance—which provides policy holders a flat amount of money to use if they fall victim to such an illness—"as more of a luxury than a risk management tool."
He said he would advise someone who could afford to pay for such coverage to get it only after they buy insurance for "the stuff they're most likely to face," naming the top priorities as health insurance, life insurance, disability insurance and long-term care insurance.
(Watch: Health insurance crisis ahead?)
A combination of those insurance plans could cover some, if not all of the extra costs associated with a critical illness. A critical illness policy would provide a flat sum of extra money available to a person suffering from a critical illness, and not be just a percentage of a person's lost wages, such as disability insurance, a Sun Life Financial spokeswoman said.
Hauserman agreed that "most people are not carrying enough coverage" of all kinds to compensate them from financial effects of a critical illness.
He noted that in 20 years as a financial planner "the number of people who have come to me owning private disability insurance I can count on one hand."
—By CNBC's Dan Mangan. Follow him on Twitter @_DanMangan.