Courts following U.S. Supreme Court precedent would conclude that the Due Process Clause of the Fourteenth Amendment incorporates the Eighth Amendment protection against excessive fines.
Courts recognize article I, section 13 of the Texas Constitution as a constitutional protection against excessive fines. A court would not enforce an unconstitutionally excessive fine. Depending on the statute, a Texas court would be obligated to follow Texas law that requires it to separate the unconstitutional fine and uphold the portion of the statute that is constitutional, if possible.
A Texas court would likely conclude that the Excessive Fines Clause of the Eighth Amendment of the U.S. Constitution is binding on the State, and federal jurisprudence is instructive about, if not determinative of, excessive fines issues under article I, section 13 of the Texas Constitution.