We design and field an innovative survey of unemployment insurance (UI) recipients that yields new insights about wage stickiness on the layoff margin. Most UI recipients express a willingness to accept wage cuts of 5-10 percent to save their jobs, and one third would accept a 25 percent cut. Yet worker-employer discussions about cuts in pay, benefits or hours in lieu of layoffs are exceedingly rare. When asked why employers don't propose job-saving pay cuts, four-in-ten UI recipients don't know. Sixteen percent say cuts would undermine morale or lead the best workers to quit, and 39 percent don't think wage cuts would save their jobs. For lost union jobs, 45 percent say contractual restrictions prevent wage cuts. Among those on permanent layoff who reject our hypothetical pay cuts, half say they have better outside options, and 38 percent regard the proposed pay cut as insulting. An estimated one-quarter of the layoffs violate the condition for bilaterally efficient separations that holds in leading theories of job separations, frictional unemployment, and job ladders. We draw on our findings and other evidence to assess theories of wage stickiness and its role in layoffs.