I would beg to differ. What would you term a chain letter? Ponzi scheme or pyramid scheme?
Social security is short (or may be short) because money was being moved from there, to pay off other benefits. Not because there aren't enough new investors. The population of baby boomers is vast, and all are paying into social security. It will survive by raising the age before people can qualify for it. The problem is also that people are living too long today. (which probably has the easiest fix of all).
I think, based on your definition, all insurance companies run Ponzi schemes as well.