Jesse Rothstein finds that the rise in disability filings in recessions is not due to people "exaggerating real disabilities or through outright fraud":
Are Long-Term Unemployed Taking Refuge in Disability?, by Ben Casselman, WSJ: The sharp rise in federal disability rolls in recent years ... is troubling to economists and policymakers because the program, administered by the Social Security Administration, is expensive, and because once workers go on disability, they rarely come off.
Economists have long known that disability filings go up during recessions, but they aren’t sure why. Perhaps the most worrisome theory is that displaced workers are essentially using disability insurance as a form of extended unemployment benefits, either by exaggerating real disabilities or through outright fraud.
University of California, Berkeley economist Jesse Rothstein set out to test that theory. He reasoned that if the increase is being driven by unemployed workers gaming the system, there ought to be a correlation between expiring jobless benefits rising disability claims. ... When Mr. Rothstein looked at the data, however, he found no such correlation. ... Mr. Rothstein’s findings ... are still preliminary...
Then why do disability rolls rise in bad times?:
A construction worker who hurts his back, for example, might be able to get a desk job during good economic times; when unemployment is high, however, making such a career switch could be much harder. Moreover, companies are much more likely to make accommodations for existing workers who become disabled than to hire a disabled worker — so a person with a disability who loses a job might well struggle to find a new one. ...
Basically, people with disabilities face a choice, apply (and likely get) disability, or continue working in another occupation where the disability is less of (or not) an obstacle. In bad times, alternatives that will allow the disabled to continue working in another occupation dry up, and the first choice -- going on disability -- is more likely. As the article notes, once this (expensive) choice is made it is generally not reversed when the economy improves.