Yes, it would essentially be a government backed loan, if necessary.

The COLA is of course tied to inflation, which is not correlated with the stock market. Technically, your SS payments can be decreased if we enter into a period of deflation; this happened once after 2008, IIRC, but the government (not sure if it was a bill they passed or what) decided to make the COLA for those years (I believe there were two of them) zero instead of having to deal with retirees seeing their SS checks decrease.

Same idea here. But keep in mind that the SS payments would still be tied to COLA, not the stock market; it's a **portion** (not all) of the Trust Fund that would be invested in the markets to increase its balance under strict guidelines (stricter than CalSTRS was under, obviously). The IOUs in the Trust Fund would still get their 1.8%-ish return from the General Fund; the rest would return 5-6% on average managed conservatively, and if you set up the balance properly, you'd have to have another Black Swan event (< 20% or more) to cause the Trust Fund to actually decrease in value, and even if it did, it would be recovered rather quickly.