Fault is typically decided and placed on the driver that caused the accident and not put on a motorist just because the person had other issues such as if their car was uninsured or their license suspended.
If the other person say ran a stop sign and hit you then normally they would be cited by the police for failure to stop and found at fault by the insurance companies. Since you were driving without at least the state required liability insurance then you may be cited by the responding officer as well for this violation of the law, though it should not have an impact on determining who is at fault.
The penalties differ depending upon state laws but could include fines, license suspension and registration suspension. Check with your state's Department of Motor Vehicles to see what your penalties may be if you were ticketed for driving without insurance.
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