Will insurance companies cover depreciated value from an accident that is not your fault if they decide not to consider your car a total loss?

I am not sure what you mean by "cover". If the car is totalled, it depends on your carrier, as to whether they will charge for depreciation. Most top A++ carriers list cars at "Agreed Value", which means you get the full replacement value for the car, regardless of depreciation.

AnswerGeico and Alstate insurance would not cover the depreciated value of my car, even though it was not my fault. I was told no one does... I don't see why, but they say there is no way to figure out how much was actually lost because your vehicle is now considered to have "one accident". I did ask several dealers if that information matters to them and they said they do take off money for accidents. sorry for the bad news, just another unfair thing in life.

Answer

Yes, if the accident was at no level your fault and the other party is accepting all liability you can send a demand lettering requesting they pay for the depreciating value of your vehicle. I would search more online how to write this, but you will need back up documentation showing the depreciation of your vehicle from at least two different dealerships. A copy of the Kelly Blue Book value will also help. I have now been in two no-fault accidents and in both cases the other insurer's company has settled for depreciation value.