Casualty and surety companies exempted from filing appeal bonds upon proof of liability – Taxable costs. Whenever an appeal is taken from any judgment in any case wherein it appears to the court that all of the particular liability of the appellant thereunder is insured against in and by a liability insurance policy or surety bond issued by any insurance company authorized to do business in the State of Illinois, and the court is satisfied of the applicable coverage of such policy or bond, it shall not be required of the appellant to provide any appeal bond or bond to stay enforcement pending such appeal, but such insurance company may be required by the court, and is hereby given authority, to execute its written recognizance of the adverse party or parties for the payment of the taxable costs of such appeal. Such company shall deposit with the court a copy of the insurance policy or bond and shall admit its liability thereunder, and agree to pay such judgment against its insured, if any, as shall be affirmed by the appellate court; and in such case the court having jurisdiction thereof, on its own motion, may enter judgment against the insurance company to such extent without further proceedings.