Tex. Tax Code § 41.4115

(a) The pendency of a protest under Section 41.411 does not affect the delinquency date for the taxes on the property subject to the protest. However, that delinquency date applies only to the amount of taxes required to be paid under Subsection (b) and, for purposes of Subsection (b), that delinquency date is postponed to the 125th day after the date one or more taxing units first delivered written notice of the taxes due on the property, as determined by the appraisal review board at a hearing under Section 41.44(c-3). If the property owner complies with Subsection (b), the delinquency date for any additional amount of taxes due on the property is determined in the manner provided by Section 42.42(c) for the determination of the delinquency date for additional taxes finally determined to be due in an appeal under Chapter 42, and that additional amount is not delinquent before that date.

(b) Except as provided in Subsection (d), a property owner who files a protest under Section 41.411 must pay the amount of taxes due on the portion of the taxable value of the property subject to the protest that is not in dispute before the delinquency date or the property owner forfeits the right to proceed to a final determination of the protest.

(c) A property owner who pays an amount of taxes greater than that required by Subsection (b) does not forfeit the property owner's right to a final determination of the protest by making the payment. If the property owner files a timely protest under Section 41.411, taxes paid on the property are considered paid under protest, even if paid before the protest is filed.

(d) After filing an oath of inability to pay the taxes at issue, a property owner may be excused from the requirement of prepayment of tax as a prerequisite to the determination of a protest if the appraisal review board, after notice and hearing, finds that such prepayment would constitute an unreasonable restraint on the property owner's right of access to the board. On the motion of a party, the board shall hold a hearing to review and determine compliance with this section, and the reviewing board may set such terms and conditions on any grant of relief as may be reasonably required by the circumstances. If the board determines that the property owner has not substantially complied with this section, the board shall dismiss the pending protest. If the board determines that the property owner has substantially but not fully complied with this section, the board shall dismiss the pending protest unless the property owner fully complies with the board's determination within 30 days of the determination.