Full coverage auto insurance on salvage title cars can be expensive, and often difficult to obtain. Generally speaking, insurance companies don’t like insuring salvage vehicles because they lose money paying out on a claim for a car that has been devalued because of serious damage. Even if documentation from certified mechanics regarding safe operating standards has been provided to the insurance company, premiums will likely be higher for salvage title cars. Unless the Department of Motor Vehicles can re-issue a clean title (laws vary by state). Liability insurance is easier to get for salvage title cars, and typically will be cheaper than comprehensive insurance.
For more info, see A Rebuilt Car Title: Pros vs Cons