If an insurance company that sells annuities fails, each state has a guaranty association that can protect policyholders. The guaranty association works with state regulators to find a new insurance company for the policyholder, and the policyholder can continue their annuity with the new company.
However, there are limits to the coverage, and the amount that can be recovered varies by state, but is usually around $100,000 per policy. Any benefits above the guaranty association's limit become claims against the company's remaining assets.