While state laws can differ in general a person is not typically found at fault for an accident due to the fact they were driving without insurance. Fault is determined based on how the accident occurred.
An insurance claims adjuster should look at the police report, witness statements and drivers' statements to determine fault. If a person was driving without insurance they should be cited by the responding law enforcement officer for this violation of the law and have to face the penalties associated with being an uninsured driver. This however is separate from being found at fault for the accident.
Fault will not usually be automatically placed on a person due to them being an uninsured motorist. For example if you run a stop sign and hit a person who had the right of way but was driving without insurance, you should be found at fault for the accident but the other driver should be cited for driving without insurance.
Since state laws do differ you can contact your state's DMV to get more information on this type of situation. In some states to further penalize uninsured motorist who are not at fault in an accident the state limits what claims they can make. This is typically known as a "no pay no play" law.
For instance in Louisiana an uninsured motorist that is not at fault in an accident cannot make a claim against the at fault driver for the first $10,000 worth of damage the car or bodily injuries sustained.