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With social security, the pool of investors is the entire country's population. This large size and government backing stabilises it. But the financials still rely on continuous population growth, forever, to work well.
The key financial metric in social security is the ratio of pay-ins to pay-outs. For example, it could be 5 paying employees for every retiree. The social security scheme has some minimum, critical ratio that is needed to maintain the tax rates and benefit levels. And if that minimum is, say, 5:1 workers to older retirees, that implies a population in a state of exponential demographic growth.
Right now, the US is propping up its lack of organic demographic growth with immigration, and accumulated trust fund savings from an earlier era. Japan had massive problems with its social security when its population stagnated.
Notice, however, that the government of Japan did not just implode like a securities fraud. This is because governments are fundamentally not like private sector criminals running Ponzi schemes.
Well, not necessarily; it relies on the average person working for 5x as long as they spend retired. If we start working at 20, and retire at 65, and the ratio is 5:1, then it allows for an average of 9 years of retirement per person before we die. The problem is that now people are living a lot longer than they were in the 1920s, which is why there's been discussion if raising the benefits age to 70. This would allow for 10 years of benefits, taking us to an average lifespan of 80 (which happens to be just about what the average lifespan in the US actually is.)
If the population is stagnant, but the age distribution remains steady, this would let the system self-sustain. It becomes problematic when there's a higher ratio of retirees to people just entering the workforce, though.