Companies almost never offer employees pay cuts in the lead-up to layoffs, despite a willingness of workers to accept even deep reductions in wages to avoid losing their jobs, a new study finds.

The National Bureau of Economic Research survey of recently laid-off workers found that 60% would accept a pay cut of 5% to keep their jobs. Meanwhile, more than half would take a pay cut of 10% and nearly a third would accept a pay cut of 25% if it meant keeping their job, illustrating the lengths to which workers would go to avoid being unemployed.

Perhaps most shocking was the fact that virtually no employers even broached the subject with their employees facing a layoff. Fewer than 3% of respondents reported having been offered a salary reduction to save their job, even though they would have accepted one. The disconnect was so stark it even left the researchers stumped.

“Employer reluctance to offer wage cuts becomes more puzzling in the face of widespread worker willingness to accept them,” they write.

Previous scholarship on the topic, such as Truman Bewley’s book Why Wages Rise in a Recession, has always suggested pay cuts were an inefficient method to avoid layoffs because workers simply wouldn’t accept them, the paper says. “Previous research leaves open the possibility that workers would simply refuse these pay cuts,” Pawel Krolikowski, a senior research economist at the Federal Reserve Bank of Cleveland, who coauthored the study, tells Fortune. “I think our paper says that’s often not the case. Workers would actually be quite willing to accept pay cuts.”

The willingness to accept lower pay in order to keep one’s job held true across gender, education levels, and experience—with one exception: Black employees were roughly 12% more likely to accept the salary reduction in lieu of a layoff. Krolikowski and his research partner Steven J. Davis, an economics professor at the University of Chicago Booth School of Business, believe this is a function of higher poverty rates among Black workers, making them more likely to “exhibit greater sensitivity” to a possible job loss that could affect their finances, they write in the paper.

Even more confounding is that workers, when faced with the possibility of being laid off, almost never initiate a conversation about keeping their job in exchange for a lower salary, even though many report being open to the idea. Only seven of 2,567 people in the survey—all of whom collected unemployment insurance benefits in Illinois between September 2018 and July 2019—said they brought up the topic.

When faced with this disconnect between the willingness of workers to accept a pay cut and the reticence of employers to offer them, Krolikowski and Davis set out to measure how many layoffs could be averted if bosses and employees were able to find a pay cut that worked for both parties. Based on their current research, 28% of layoffs could be avoided just by offering a willing employee a pay cut they deemed acceptable. They estimate the number could be as high as 35%, but proving that definitively would have required a better understanding of the exact circumstances of each respondent’s layoff. Avoiding these layoffs would be in the “joint interest of worker and employer,” Krolikowski and Davis write, because the firm would still get to reduce cost, while the employee would keep their job—the benefits of which are obvious.

The hard evidence that almost 30% of layoffs could be avoided just by lowering an employee’s salary makes the almost total absence of these conversations even more baffling. When asked why this might be the case, Krolikowski posits it’s because employers are hesitant to cede control of personnel decisions to employees. “Employers can choose which workers to lay off; they can’t do that in the case of a pay cut,” he says.

As part of the research, Krolikowski and Davis asked the laid-off workers they surveyed who would have agreed to a pay cut why they thought their employer didn’t raise it as an option. The top answer with 38.9% of responses was, “I don’t know.”

“This result suggests that many job losers don’t understand the business considerations that led to their layoffs,” the paper states.

However, the second most common response, ”it would not have prevented my layoff,” which 36.3% of respondents selected as the reason they believed their employers didn’t offer wage reduction, illustrates the reality that not all layoffs are made for purely cost-cutting reasons. Some might occur because an organization has shifting priorities and wishes to replace workers from a division it no longer considers essential with headcount in another part of the firm. Krolikowski acknowledged this and called it an “important question” but declined to comment further because it was outside of the scope of the study.

The other reasons employees believed they weren’t offered pay cuts point to considerations about the firm’s overall productivity. Eight percent of respondents cited two potential explanations: fears that the best workers would quit and that lower salaries would undermine morale. “Productivity suffers when workers feel insulted or wrongly treated by their pay,” the paper states.

In this scenario, the thinking goes, the firm would be worse off with a host of disgruntled employees rather than being perpetually short-staffed as a result of mass layoffs. The paper cites a case study of the tire manufacturer Firestone, which involved a recall of 14 million tires that coincided with the announcement of impending wage cuts in an upcoming union contract.

There’s also the practical matter of predicting who the unhappy and unproductive workers would be, Krolikowski adds. “If these workers can be identified in advance, then the best policy might be to lay them off and propose a pay cut for others,” he says. “But if they can’t be identified in advance, or if it isn’t feasible to selectively fire these workers, then broad layoffs may be the best action.”

Another reason why cutting pay in exchange for jobs is so rare is that it could set a precedent: Employees might ask for raises when performance is strong, and firms might ask for pay cuts whenever they please. “Could they always come and say, I want a pay cut, even when times weren’t bad?” Krolikowski says. Those “firms seeking a pay cut might not be credible.”