You might be able to remove your truck from your car insurance policy without spilling the beans about your roll-over accident if it was a single-car accident.  However, it doesn’t mean your insurer won’t find out about the accident another way.

If the police made a report on the accident and your state places accidents on your driving record, your insurer will find out the accident the next time it pulls your record, whether you still own that vehicle or not.

Also, your car insurance company may ask why you’re removing your truck.  Honesty is always the best policy since you don’t want to be looked at later for misrepresenting facts. 

You’re correct that liability insurance doesn’t cover damage to your own vehicle, so you’re unable to make a claim for the total loss of your truck.  If you damaged another party’s property in your roll-over accident (such as another car or, say, a person’s fence) it would be covered by your liability insurance — up to your limits.  And, if you’re trying to keep the accident a secret from your insurer, unfortunately that won’t happen if another party makes a claim against your liability coverage.

If you had collision insurance on the truck, you could have made a claim for its actual cash value since the “upset” of a vehicle is covered by this optional coverage.  Keep this in mind when buying a replacement vehicle and deciding upon which car insurance coverages you should choose.