If you own a car but can't afford to insure it, your options depend on your state's laws and insurance agency policies. Most jurisdictions allow someone who doesn't have title to a car to insure it. However, most insurance companies won't write the policy under those conditions. Unless you have an "insurable interest" in the car, you'll have a hard time getting a policy and making a claim. Insurance companies have several reasons for that policy, but it all boils down to minimizing their risk.
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Insurance companies want drivers to have an insurable interest in the car, meaning that drivers personally have a stake in protecting it. If someone else is insuring the car in your name, insurance companies worry that you'll be more likely to damage the car and pocket any claim check you receive. Insurers also want to keep those with an excellent driving record from using their own data to buy insurance for other, riskier drivers, thus providing a false picture of the risk the insurance company is taking when it writes the policy.
Even if your state and insurance company allow another individual to insure your car, this puts you at greater risk that a claim will be denied. Insurance companies require the claimant to demonstrate how she sustained a loss in order to benefit from the policy. If the person insuring the car has no basis for financial harm, there's no reason to pay out the claim. Therefore, if someone else is insuring your vehicle and you get into an accident, the insurance company may determine that the policyholder didn't suffer a financial loss even though the vehicle was damaged, since the policyholder doesn't own the car in question.