The Finance Ministry was a government department in the Cardassian Union, responsible for the Union's finances and economy. The Finance Ministry controlled taxes, and was apparently capable of exiling people who refused to pay them.
In 2371, an attempt was made on Elim Garak's life. When Odo asked him whether it might have been related to the reason Garak was exiled, Garak said that he doubted the Finance Ministry would try to kill him because of his failure to pay his taxes. Odo didn't believe a word of his story, but Garak claimed he would not lie about something like that, saying he wasn't proud of it. (DS9: "Improbable Cause")