Yes, your deductible amount would normally be due if you are using your own insurance coverages to claim the damage to your vehicle. Fault has nothing to do with if a deductible is due usually. If your vehicle was hit by another car which was driven by a carjacker then you would make a claim through your collision coverage and thus owe the deductible associated with this physical coverage.

Since the car was stolen from the car owner they would not be liable for the damages the thief caused when being pursued by police since obviously the carjacker did not have permission to drive the vehicle. State laws differ but normally the person whose car was taken is not found responsible because they did not give the thief permission to drive the vehicle. Thus the car was out of the owner's control when it hit your vehicle.

If there is no liability on the owner of the stolen/carjacked vehicle, since typically they are not held responsible for the acts of a thief in their car, their insurance company would not accept claims on the property damages claims of those affected by the person who stole the vehicle.

If the carjacker was caught then he or she should be held responsible for their actions while in the vehicle that they took without permission. Of course their own insurance, if the thief had car insurance of their own, would not cover this either since the carjacker was committing a criminal act.

There are some situations in which a car insurer will waive a deductible so you can speak to your agent and/or claims adjuster to see if your insurance provider ever waives the deductible amount. If you do have to pay it you can seek legal advice on if you can pursue the carjacker in court so that you can seek a judgment for your deductible amount and any other expenses you incurred as a result of this incident and that your insurance company did not take or reimburse you for.

If you read through the terms of your auto insurance policy it should state under what situations your deductible would be due and find that you will owe your deductible no matter the fault if you use your collision coverage. If you want to get information on your state's insurance laws and if there are any situation in which you state requires an insurance carrier to waive a deductible, contact your state's insurance regulator.