(a) Within the period prescribed by Section 481.307, a person who files a petition for judicial review may:
(1) stay enforcement of the penalty by:
(A) paying the penalty to the court for placement in an escrow account; or
(B) giving the court a supersedeas bond approved by the court that:
(i) is for the amount of the penalty; and
(ii) is effective until all judicial review of the order is final; or
(2) request the court to stay enforcement of the penalty by:
(A) filing with the court a sworn affidavit of the person stating that the person is financially unable to pay the penalty and is financially unable to give the supersedeas bond; and
(B) sending a copy of the affidavit to the director by certified mail.
(b) Following receipt of a copy of an affidavit under Subsection (a)(2), the director may file with the court, before the sixth day after the date of receipt, a contest to the affidavit. The court shall hold a hearing on the facts alleged in the affidavit as soon as practicable and shall stay the enforcement of the penalty on finding that the alleged facts are true. The person who files an affidavit has the burden of proving that the person is financially unable to pay the penalty or to give a supersedeas bond.