28 U.S.C § 2101 (stay of execution pending application for writ of certiorari)
...
(f) In any case
in which the final judgment or decree of any court is subject to review by the
Supreme Court on writ of certiorari, the execution and enforcement of such judgment
or decree may be stayed for a reasonable time to enable the party aggrieved
to obtain a writ of certiorari from the Supreme Court. The stay may be granted
by a judge of the court rendering the judgment or decree or by a justice of
the Supreme Court, and may be conditioned on the giving of security, approved
by such judge or justice, that if the aggrieved party fails to make application
for such writ within the period allotted therefor, or fails to obtain an order
granting his application, or fails to make his plea good in the Supreme Court,
he shall answer for all damages and costs which the other party may sustain
by reason of the stay.