Last year, Neal Gabler wrote in The Atlantic about Americans’ financial instability, noting that nearly half of them would have a hard time coming up with $400 to cover a sudden expense. That’s bad news, not least because many unexpected events—from an illness to car or home repairs—can lead to bills that amount to much more than that. A recent report finds that many American families can spend about half of their monthly income covering such expenses, with the median cost being around $2,000.

The report, put out by Pew Charitable Trust, includes the results of surveys conducted in 2014 and 2015 to see how Americans were coping with what are referred to as financial shocks—those one-off expenses that crop up from time to time. Pew found that in large part, Americans’ ability to weather financial shocks is partially dependent on something that Americans still struggle to accumulate: savings.

According to the report, savings can trump income when people have to deal with unexpected expenses; having $2,000 in savings allowed those in the lowest income brackets to recover from these events as quickly as those who made more money, but had less in savings. For example, around three-quarters of families that earned less than $25,000 but had $2,000 to $4,000 in savings said that they had a hard time recovering after a financial shock. That’s around the same proportion of families who said they had a hard time recovering even though they earn more—between $25,000 to $84,999—but had less than $2,000 in savings.

While this illustrates the importance of saving up cash, that’s often easier said than done. This is in part because while people of all income levels can live paycheck-to-paycheck, those barely earning enough to cover necessities have a much harder time whittling down their expenses. And those who earn the least are also the least likely to suddenly inherit a sum of money or have family members or acquaintances who can help them out in a bind. That can make their ability to save dependent upon working more hours, or getting raises, or finding the time and money to advance their education—all difficult feats.

And the truth is that while savings helps in an emergency, it isn’t enough to ease financial stress. While cash on hand prevented many families from being completely destabilized by an emergency, about half of those who had to shell out their saved money reported feeling financially strapped in its aftermath.

The fallout from experiencing a sudden expense—especially among low-earners—has a cyclical effect: 70 percent of those who had a financial shock in 2014 also had one in 2015. Being a millennial, making less than $25,000 a year, or being black or Hispanic also made the likelihood of experiencing a financial shock and struggling afterward much more likely in both years.

Financial hardship can leave some families with few good choices. While just under two-thirds of those surveyed said that they would use their checking or savings accounts in an emergency, about 35 percent of people said that they would use their credit card. Of those who did rely on credit, less than a quarter said they were able to pay off the balance in a month or less, which pushed up their revolving debt. Not coincidentally, high debt levels in 2014 were an important predictor of whether or not a family would face financial hardship in the following year.

Breaking this cycle would be tricky. It would require not only better wages for many workers, but also different systems for savings and an understanding that even fiscal responsibility can’t ward off every financial threat.