No, Uninsured Motorist coverage will not cover your vehicle being stolen. Uninsured Motorist coverage is normally for Bodily Injury though Uninsured Motorist Property Damage is available in some states. Where it is available UMPD covers when your vehicle when an uninsured collides with you, not if an uninsured person steals your vehicle.
For the theft of your vehicle you would need Comprehensive coverage. Comprehensive covers your vehicle for losses resulting from incidents other than collision. For example, Comprehensive insurance covers damage to your car if it is stolen; or damaged by flood, fire, or animals. Pays to fix your vehicle less the deductible you choose.
The person that stole your car did not have insurance however even if they did it would not have covered their criminal act of stealing your car and totaling it in an accident.
You may want to contact legal counsel to determine what your rights are. Since the person that stole your car was caught you may see if it is possible to sue this individual for the value of your car that he or she stole and totaled out in a wreck.
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