Many people first become aware of disappearing deductibles from the Nationwide vanishing deductible commercial (a vanishing deductible is exactly the same as a disappearing deductible) which is a major component of the Nationwide Insurance TV campaign.
While Nationwide is the company that is promoting their vanishing deductible, they aren't the only insurance company that offers a disappearing deductible with their car insurance. If you are unsure whether your car insurance company offers disappearing deductibles, you should contact your insurance agent and ask. It costs nothing to do so and while a company may offer it, they may not automatically provide it. Also be aware of the disappearing deductible catch to make sure this product is right for you.
Nationwide also came out with a second vanishing deductible commercial featuring a character named Carl titled "Vanishing Act":