Fresh efforts to shrink state-run Citizens Property Insurance Corp. and the Florida Hurricane Catastrophe Fund, the state’s reinsurer of windstorm risk, could push more property insurance companies and policyholders alike into the private sector for protection.

Friday is expected to mark the end of the seventh consecutive Atlantic hurricane season without a named storm hitting in Florida, but windstorm insurance could get more expensive for many Florida property owners next year if the state allows private insurers and reinsurers to sell more coverage.