Insurance can't work if either all or none of your customers are going to file a claim, because the premise of insurance is that those who don't file claims pay for those who do. This insurance would have to charge a premium that would cover the "everyone files a claim" case, which means people would be paying N dollars in order to have a chance of getting their N dollars back. Not a good deal ;-)
This isn't necessarily the case. Life insurance insures against certainty.
I think one things which would make this idea feasible is the fact that people are old by the time they receive SS so a certain percentage (a somewhat predictable one) will be dead. If a high enough percentage is expected to be dead, you could create rates which would allow you to win over the long run.
You could also make the SS insurance apply only to the individuals and not their beneficiaries who would have received the SS benefit in the event of the individual dying prior to receiving benefits.
Right, unless the insurance company can hedge their bets. At it's simplest they could insure themselves with a re-insurance company.
They could also figure out financial consequences of social security going away and place long term bets on that. If they are able to hedge properly, they're basically reselling that hedge.
I... honestly am not qualified to say that this is what it is, but I would strongly suggest taking a look at the details of how we entered this recession. It sounds extremely familiar.