I drive a car with a reconstructed (salvaged) title, and my insurance company was willing to insure it for liability only. I wanted to put comprehensive coverage on it, but they said the value of a non-reconstruct of the same model was so low that the one I owned was not worth the added coverage. Essentially, they made it sound like they were doing me a favor by not taking my money. :-D
The willingness to cover probably varies by company, vehicle, and quality of restoration. If the company was willing to insure it (for collision/comprehensive), they undoubtedly would require an inspection of the vehicle prior to coverage.
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