party and a cash deposit in the required amount is not timely made or a sworn statement of inability to pay is not timely filed, the judgment of the justice court becomes final and a writ of possession and other processes to enforce the judgment must be issued on the payment of the required fee. If the landlord is the appealing party and a cash deposit is not timely made or a sworn statement of inability to pay is not timely filed, the judgment of the justice court becomes final. If the appeal bond is approved by the county court, the court shall transmit the transcript and other records of the case to the justice court, and the justice court shall proceed as if the appeal bond was originally approved.