I'm not exactly sure what you're envisioning or who "they" are. However:What about (does not apply in the case) they are under insured? In an accident case where at fault is clear? They then have to go to their Comprehensive/ UIM coverage to get their damages covered> how does that affect rates?
1. Comprehensive is coverage that pays for replacement or repair of a vehicle as a result of something that's not a "collision," so it wouldn't generally be implicated in the case of a car accident.
2. If one has uninsured/underinsured motorist coverage, it works more or less the same way as when the insured makes a third-party claim against the other driver's liability coverage. Stated differently, the UM/UIM coverage substitutes for or supplements the liability coverage that the other driver doesn't have or which is insufficient.
3. A not-at-fault claim against one's own collision coverage should not impact one's premium (in fact, I believe it's illegal for such an impact to occur -- at least in CA -- but I'm not certain of that).