In the event an auto accident should occur, find out more from the Office of the Insurance Commissioner about how the auto insurance claims process works. Here is everything you need to know about subrogation claims, a type of thirdparty claim.How Long the Process Takes. How subrogation claims work in car accident and personal injury. How long subrogation takes and your rights when car or health insurance seeks to subrogate. The process of insurance subrogation is often easier to understand with an example: Jane is involved in a car accident in Yakima. Please use this form to submit a complaint about an insurance company. The Plaintiff, above named, complaining of Defendants, above named, alleges and says as follows: 1. Please use this form to submit a complaint about an insurance company. Subrogation is the right of an insurer to pursue the party that caused the loss to the insured in an attempt to recover funds paid in the claim.