With an array of serious health problems, James and Dolores Smith take a combined 17 prescription medications, some which cost $300 apiece for a month's supply.
Insurance had covered much of the Smiths' prescription costs, but not all, leaving the couple on the hook for $2,000 in out-of-pocket payments annually.
When 64-year-old Dolores lost her job and employer-provided insurance last winter, the Oswego, New York, couple maintained their prescription-drug buying by relying on a sympathetic pharmacist who extended them credit. They also put other non-medical purchases, including food, on credit cards. But that debt soon became unmanageable for the couple, whose combined income is less than $45,000 annually.
Read MoreHow not to go broke buying prescription drugs
"I was paying the pharmacy what I owe, but I had a hard time paying my credit card bills," said Dolores, who suffers from chronic obstructive pulmonary disease, partial heart blockage and extreme anxiety. Her 79-year-old husband has congestive heart failure, kidney failure and COPD as well.
"Without the insurance, it was real tough," said Dolores, who stopped going to her pulmonologist and heart specialist during the time she lacked health coverage.
The couple got some relief in March, when Dolores signed up for an individual insurance plan under the Affordable Care Act. James is on Medicare, which she said "helps a lot."
But Dolores' plan has a $241 monthly premium, combined with annual deductible of $1,750. Those out-of-pocket expenses added to the couples' increasingly difficult financial juggling.
On March 16, the Smiths' lawyer, Robert Fix, filed papers in federal court seeking Chapter 7 bankruptcy protection for the couple.
About half of Fix's bankruptcy clients have medical-related debt, and often have credit card debt that stems from having had to pay for prescription medication out-of-pocket, his office said.
Read MoreWhen staying healthy forces you to break the law
In 2013, the federal government reported that Americans had $41 billion in out-of-pocket costs associated with prescription drugs.
And those prescription drug costs will continue playing a key role in medical-related debt and bankruptcies despite the expansion of insurance for millions of other people under the Affordable Care Act, experts told CNBC.
Even though more people will be getting their medications covered by insurance, those experts noted a growing trend in both the individual insurance market and the employer-provided market toward having insured people pay an increasing share of medical costs, including their prescriptions.
And that makes being aware of strategies to stay out of debt and bankruptcy court as important as ever for people on medication.
Yet many people, particularly those with lower incomes, are unfamiliar with the myriad of health insurance terms that play a role in how much they pay for drugs. Consumers also have a hard time deciphering insurance plans' offerings. That lack of knowledge increases the likelihood that consumers, especially those new to insurance, will make choices that put them at risk of burdensome medical debt.
A report last year by the price comparison site NerdWallet found that medical debt was the single leading cause of U.S. bankruptcy filings, and that 56 million Americans would have problems from medical bills. A new report last week by the Consumer Financial Protection Bureau found that 52 percent of accounts sent to collection on people's credit reports stemmed from medical-related debt.
Read MoreFor patients, costly Hepatitis C medication is priceless
Prescription costs play a big role in those bills for millions of Americans who, as the federal Centers for Disease Control noted in its 2013 report "Health, United States," increasingly use drugs "in the long-term treatment of chronic conditions, including hypertension, high cholesterol, and diabetes, which are major risk factors for heart disease."
The prices of those and other drugs remains out of reach to many.
Commonwealth Fund analyst Sara Collins noted that in an oft-cited survey the group released last year. In the survey, people were asked if they had gone without medication in the past 12 months because of costs.
"About 27 percent of the adult populations said 'yes' to that question," Collins said. "An estimated 50 million people."
"Among people who were insured, about 21 percent said 'yes.' Among people who were uninsured, about 43 percent."
Collins said the level of medication-skipping is worrisome, particularly among people with chronic conditions, because if those people don't keep their conditions in check "it leads to long-term health problems....In the long run, you contributed to the higher costs of the health system overall."
For millions more people who do buy medication, the dollars they spend for the drugs stretch their household budgets, particularly if they purchase these drugs with credit cards with high interest rates, and don't pay off the balance each month.
"It can be very costly," said health-care affordability expert Mark Rukavina, founder of Community Health Advisors, which consults with hospitals on financial assistance, billing and debt-collecting practices. "It can be burdensome."
Rukavina noted that unlike bills from doctors and hospitals, prescription costs have to be paid before the person can obtain the drugs they need.
"Generally speaking, it's like cash on the barrelhead to get the medication," he said. "People will often put it on a credit card."
Read MoreObamacare hasn't cured drugstore sticker shock
While insurance plans will cover some or most of the medication, more plans are requiring people to be responsible for an increasing out-of-pocket shares of the costs, Rukavina said. Although that trend has been going on for some time among all types of medical insurance, relatively high out-of-pocket responsibility is a notable feature of many individual insurance plans under the ACA.
And health plans, both under the ACA and employer-based, often will require customers to pay higher co-payment or higher percentage of co-insurance for pricier, specialty drugs, Rukavina said. He added that such "tiered" out-of-pocket costs are particularly worrisome to cancer patients, who often require treatments and medications for years.
Although the price of drugs is not necessarily negotiable, Rukavina said peoples' ways of dealing with the costs often get them into deeper debt than they need to incur.
And "what I've seen more and more is that" people getting treatment for serious health problems feel compelled to pay to their medical bills first and are "foregoing paying other bills because they don't want to offend the doctor," believing mistakenly they are putting their treatment at risk if they do so, he said.
By putting more non-medical purchases on credit cards, exhausting their savings and borrowing from friends, he said, they are incurring an ever-increasing amount of debt that pushes many people to a financial brink, and often farther into bankruptcy court.
Rukvina urged people to negotiate with their medical providers on costs, explore whether hospitals and pharmacy manufacturers offer assistance programs on prices, and to make sure their insurance plans are paying ever cent of the health benefits they are obligated to.
Read MoreWhy there's no end in sight for higher drug costs
It remains to be seen whether under the ACA, which subsidizes individual insurance plans for millions of people,and bars insurers from discriminating against people with pre-existing conditions, will lead to more consumers managing their drug-related costs better.
Mitch Rothschild, the CEO of Vitals, a company that among other things helps health plans give their members access to to cost and quality transparency tools, said that individual plans under the the health-care law will give many of their buyers "sticker shock." Consumers will realize the true cost of their medical care, including prescription drugs, because of their often-high deductible amounts.
Rothschild also noted that individual plans sold on the ACA exchanges have different ways of presenting their prescription drug coverage options, raising the possibility that consumers will end up with bigger-than-expected drug bills.
"The ones that I've looked at it, it's very confusing to do a plan-by-plan comparison," he said.
Rothschild also noted that "people are tending to go with the least expensive option" when buying a plan under the health-care law, meaning they will opt for the plan with the lowest monthly premium.
But different deductible levels between plans, as well as how the out-of-pocket payment schedules are structured, he said, can leave price-conscious shoppers with bigger drug bills than they would have at first expected.
"Before you go to seek Medicare care, know the cost out-of-pocket to you," Rothschild urged.
—By CNBC's Dan Mangan