The U.S. government has two main programs that give money to nonelderly, nonworking adults. One is unemployment insurance, which you only get if you're actively seeking a job, and the other is disability insurance, which you only get if you're physically or mentally unable to work. In theory those should be hermetically sealed populations. In practice, as unemployment insurance expires, people seem to suddenly become disabled:
Since 1995 the number of disabled workers has doubled and expenditures have increased even faster than disabled workers, tripling since 1995. The increase in workers receiving disability insurance has come at the same time as the U.S. working-age population has become healthier. A large fraction of the increase in disability has come from increases in hard-to-verify back pain and mental problems (see Autor and Duggan and more recently Autor).
Now one way to take this would be to slam all those lazy layabouts collecting disability insurance, but I think it really serves to underscore the weakness of other aspects of the American safety net. The first and best form of insurance against involuntary unemployment is supposed to be full employment. You work for a company that's mismanaged and goes out of business. You lose your job. Some other, better-managed firm is expanding and hires you. Technology displaces some jobs and creates other new ones. A properly managed macroeconomy provides work. The macroeconomy of 2008-11 has not provided work.
Second we see that cutting off unemployment-insurance benefits in an effort to force workers into jobs that don't exist is a bit of a fool's errand. In normal times, unemployment insurance serves as a valuable bridge that helps workers avoid under-matching into jobs that don't fit their skills. In times of prolonged economic slack it doesn't work as well, but cutting unemployment insurance benefits off has perverse consequences. A better approach would be to go bigger on the underlying concept of unemployment insurance with a comprehensive wage insurance program that recognizes that the range of labor market risk people are exposed to goes beyond a simple has-a-job/doesn't-have-a-job dichotomy