Hi - I practice in Mississippi.
The statute you're referring to says:
§ 11-33-95. Judgment for damages pleadable as payment.
The judgment in favor of the defendant against the plaintiff for the damages assessed and the costs may be pleaded by the defendant as a payment in the same action, or in any other suit on the same cause of action on which the attachment was sued out. An execution shall not be issued on such judgment until after the dismissal of the action or final judgment on the merits. If the action be dismissed, or if, upon a trial on the merits, judgment be in favor of the defendant, without his having obtained the benefit of the judgment in his favor for damages and costs, he shall have execution of said judgment in his favor. If the plaintiff recover in the trial on the merits, and on such trial the defendant did not avail of his judgment against the plaintiff for damages and costs, the greater recovery shall be credited with the sum of the smaller, and judgment shall be rendered by the court in favor of the party to whom the difference may be due.
The only reported case on this statute says:
Where defendant recovers a judgment for damages, and plaintiff's action thereby abates and the assignee of such judgment seeks to enforce it, plaintiff though his claim has meantime become barred, the defendant being insolvent, may resort to equity to enforce his right conferred by § 2756 Code 1880, to use said claim defensively as an offset against the judgment. Feld v. Coleman, 72 Miss. 545, 17 So. 378.
This statute does not deal with staying the payment of a judgment in the sense you're referring. Instead, it talks about how a defendant, which is awarded damages in a case, can collect the damages from the plaintiff.
It is basically saying that the plaintiff cannot collect a judgment against the defendant if a greater judgment was rendered against the plaintiff in favor of the defendant.
Unless the defendant was awarded damages, this statute doesn't apply.