Ponzi schemes have the defining characteristic that returns to the first batch of participants are paid from the money invested by the second batch. But, not everyone loses - those who get out early often do quite well. What ends up as a fraud can start off innocently enough with funds earning more than enough to meet the returns promised investors. It's when the promises continue unabated, and returns fall, that the fraud occurs. The new money is used to keep the old promises leaving nothing for new investors. A downward spiral begins, eventually the returns fail to keep the old promises, people want their money out and all collapses. The frauds have been going on for centuries, long before Ponzi.
A new concern is whether something similar is happening in some pension plans. An Economist article highlighted some of the concerns over public sector employee pension plans and likened them to Ponzi schemes:
"In Britain some national schemes are “unfunded”: that is to say, the government does not put aside a specific pot of cash to meet its liability to its employees. Instead, it vows to meet the cost out of future taxation. Such “pay-as-you-go” schemes, as they are known, are rather like the pyramid schemes made famous by Charles Ponzi, a 1920s swindler, in that they need a continuous stream of new investors to meet the claims of the old ones. (Of course, many basic state old-age pensions work in the same way.)"
This may overstate the case with respect to most public sector employee pension plans. A key element in the classic Ponzi scheme, apart from misrepresentation, is unsustainability. The reason Madoff Investment Securities finally collapsed was that it could no longer pull in enough new investors to supply the funds to pay off the existing participants. But, in the case of the public sector plans there is usually a contributor of last resort and that is the sponsoring government. While there have been a few cases in the US where the governments (or taxpayers) have said "no more", they are not common. The issue with public sector plans is their gross understatement of costs - not the security of benefits.
The plans where security is in question, and which probably come closest to Ponzi schemes are some target benefit plans. These plans typically have fixed contributions - by contract or union negotiations - and defined benefits. Some of these plans have attempted to maintain this balance using too high an expected investment return. These have had to cut benefits, some dramatically, because the combination of contributions and earned investment return was not sufficient to deliver the benefits promised. This combination makes the plans unsustainable at promised benefit levels and the reduction in benefits hurt members. But, like Ponzi schemes, those who left early enough, before things came to a head, did OK - they got a good settlement value. The issue is that those who stayed, whether active or retired, found their benefits cut and this came as a big surprise. The sponsors argued that they made no certain promises to members and that all was dependent on investment earnings, but I suspect Madoff said the same thing.