It’s possible but unlikely that you would lose all of your money in an annuity. There are two possibilities:
Investment losses — Variable and indexed linked annuities don’t guarantee principal. It’s possible for market losses to reduce the account substantially.
Insurance company failure — The deposits of fixed annuities and fixed indexed annuities are invested in the insurance company’s general account, subject to creditors’ claims. It’s theoretically possible for an insurance company failure to exceed the resources of a state guarantee fund.