Yes, a renters insurance policy covers goods in a storage container. Renters insurance protects your interests wherever in the globe. You will be covered even if you reside in one state and keep your belongings in another. A renter's insurance coverage protects your possessions in your house against certain risks. The same coverage is provided for objects kept in a storage facility. For example, if a fire breaks out at your storage unit and damages the contents within your unit, your insurance provider will reimburse you for the cost of replacing them.