Can I switch to another auto insurance company?

My current auto insurance carrier is Geico in California. I had an at- fault accident in last Nov and the claim that I filed to Geico is still open because in the accident there were totally three cars involved and one of the other two persons never spoke to my insurance company and claimed anything. My coverage is enough in case that person comes back. Due to this accident, my premium is dramatically increased. I got several much lower quotes from other auto insurance companies for my next renewal in mid Feb. My question is: if I change to another auto insurance company while the claim is still open, will Geico still take care of the claim, i.e., pay the person if he comes back? Thanks very much for any information.