What does it mean for society as a whole to "save money"? It doesn't mean anything because all money is debt. It is both an asset and a liability. You can try and indebt the future generations by promising to tax them, but future generations may or may not honor that debt. Of course, in any case, debts that cannot be paid, will not be paid.
It is in bad taste to turn a moral obligation (taking care of the elderly) into a financial obligation. We would recoil at the idea of family members sending bills to one another. The older generation looking down and saying you have to take care of us, because we said so, or because you owe us a financial debt, may not carry as much weight as the simple moral obligation.
Now what the older generation, CAN save, is productive capital: infrastructure and machines. That can increase productivity of the working generation to help them support the retired generation, but only up to a point.
The older generation ultimately passes down to the next generation all of their capital, including all government lands and unused resources.
If money represented capital, instead of debt; if it represented the accumulated capital of society, then it WOULD represent the capital that could be saved and then purchased or inherited by the next generation and used to support retirees.