Incredibly low for a number of reasons.
First, insurers are highly regulated by state insurance regulators that constrain the types of investments that they can make and require a certain amount of capital. The insurers have to do quarterly reporting to insurance regulators and more extensive annual reporting which is audited, typically by one of the big four accounting firms and are subject to a more detailed examination by insurance regulators every 4 years or so. If an insurer's capital declines below a certain level, then the regulator will require a company to submit a plan as to how they intend to remedy the situation and if accepted, the plan is monitored. If the insurer's capital continues to decline, there are a defined succession of interventions that would occur, the most extreme of which would be the regulator taking over the insurer. In theory, even if an insurer is taken over the insurer may still have sufficient assets to fund its liabilities. In many cases the regulator will find a more healthy insurer to assume the less healthy insurer's policies, or the regulator will manage the in-force policies as they run off the books.
Second, in the unlikely event that the intervention isn't quick enough, then state guaranty funds would help provide for any deficit of liabilities over assets. These state guaranty funds are funded via assessments on healthy insurers. A paper published by the National Organization of Life and Health Insurance Guaranty Associations addressed the systemic risk as follows:
"..... could the guaranty system meet its obligations if the crisis resulted in the simultaneous failure of several nationally significant insurers?
The answer from historical experience is “yes.” During the last major wave of life insurer insolvencies in the early 1990s, the guaranty system protected all consumers to whom it had responsibilities when confronted with the simultaneous resolutions of three nationally significant insurer failures (Executive Life Insurance Company, Mutual Benefit Life Insurance Company, and Confederation Life Insurance Company), plus a number of failures involving middle-tier and smaller companies. At no time – not even in the most expensive years – did the cost of protecting consumers even remotely approach the assessment capacity of the guaranty system."
Third, in addition to the above, most major insurers are given financial strength ratings by the major rating agencies, and the capital requirements to get good ratings are even higher than what regulators demand (typically 3-4 times the level where regulatory interventions would begin).
To the best of my knowledge, there have not been any
significant insurance company failures since the risk-based capital regulatory system was put in place 15-20 years ago.
(AIG's problems were at the unregulated parent company, its regulated insurance subsidiaries were not part of the problem. In fact, they were part of the solution because the proceeds from the sale of many of AIG's insurance operations provided funding for AIG's repayments to the US treasury).
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