Equitable Life - large insurance company collapsed after attempting to reneg on contractual guarantees it had given to its clients, mainly lawyers and accountants who took them to court and won or, depending on how you look at it, lost because they caused the collapse.
AIG - even larger insurance company ran into massive financial difficulties during the financial crisis.
If an Insurance Company goes down (which rarely happens - they tend to be bought by another company) your assets are held on the balance sheet of the Insurance Company, you are a creditor in a long line of creditors.
With a SSAS you will have a Trustee and typically a separate custodian structure such as Pershing.
This separation of roles and responsibilities makes for a more transparent structure (certainly from a cost disclosure perspective) compared to an Insurance Company providing a pension in Ireland today. But be aware, that the same functions are all happening within the Insurance Company, you just don't see them. I wrote about this in the Sunday Business Post around the time of the collapse of Custom House Capital.
From a risk management perspective, what matters is where the legal title to the assets is held and how secure that is.
Pershing, for example, has Assets under Custody globally of around €1.7 Trillion
That's such as staggeringly large number that a reference point may help.
How big is a trillion?
If €1 = 1 second then 10 minutes ago is €600
€1M = 12 days ago
€1billion = May 1986
€1 trillion = 29,693 BC