My understanding is that "collision insurance" covers damage to your vehicle when you are at fault. I don't think that that's relevant here.

My understanding is that there is also something separate called "uninsured driver" coverage which covers damage that should be covered by the other driver's liability insurance in cases where the other driver isn't properly insured. Do you have that? (it's usually very cheap)

Basically you should be covered by either the other driver's liability coverage or, if that doesn't exist, your uninsured driver coverage.

It's also possible that I'm completely wrong. Read your policy carefully.