Millions of unemployed Americans like Mr. DeGrella have trained for new careers as part of the Workforce Investment Act, a $3.1 billion federal program that, in an unusual act of bipartisanship, was reauthorized by Congress last month with little public discussion about its effectiveness. Like Mr. DeGrella, many have not found the promised new career.

Instead, an extensive analysis of the program by The New York Times shows, many graduates wind up significantly worse off than when they started — mired in unemployment and debt from training for positions that do not exist, and they end up working elsewhere for minimum wage.

Split between federal and state governments — federal officials dispense the money and states license the training — the initiative lacks rigorous oversight by either. It includes institutions that require thousands of hours of instruction and charge more than the most elite private colleges. Some courses are offered at for-profit colleges that have committed fraud in their search for federal funding. This includes Corinthian Colleges Inc., which reached an agreement last month with the federal Education Department to shut down or sell many of its campuses.

The Times examination, based on state and federal documents, school and court records, and interviews, shows that some of the retraining institutions advertise graduation and job-placement rates that often do not hold up to scrutiny.

The idea of dividing responsibility between federal and state officials was to give local and state authorities more power in helping the unemployed in their areas. But the unemployed who sign up for training are often left to navigate a bureaucratic maze with almost no guidance. To avoid any appearance of favoritism, federal job counselors are not allowed to recommend schools to job seekers, leaving many of the unemployed to unwittingly select institutions that are expensive, have a history of legal trouble or are academically substandard.