Except in rare local cases, the land owner is not required to provide proof of insurance to the renter. Landlord insurance covers the structure of the home and walkways leading to the domicile, along with things such as major appliances and coverage protecting against fire or water damage. For the purposes of insuring the property, landlord insurance and property belonging to renters are two completely different cases, and neither party is required by law to report having insurance coverage to the other party.
Natural disasters are not typically covered by landlord insurance. For that coverage, the land owner will need to purchase a plicy specifically designed for the type of disaster being insured against. In some cases, such as purchasing flood insurance in Florida or earthquake insurance in southern California, the disaster coverage must be purchased separately from other coverage and may only be available through high-risk insurance pools or pools established by your state department of insurance.
The property of the renter is not covered by landlord insurance. The renter needs to purchase renters insurance or personal property insurance to have their possessions covered. Even if the home is destroyed by a fire, the insurance of the landlord does not extend to the renter, and any losses the renter suffers are incidental as far as the landlord is concerned.