Assuming you are using a friend's car with their permission and it was stolen while the keys were in it, their comprehensive coverage should cover the vehicle. However, certain exclusions may apply. Ultimately, the claims adjuster would determine if this loss would be covered.
Comment Update: The claims process varies by company. You can expect it to take 3 to 30 days depending on the situation. You will need to keep your payments current until the lien has been settled. You may want to consider GAP insurance too.