(a) A judgment perpetuating and foreclosing a tax lien may be transferred and assigned for the amount of the taxes covered in the judgment and may be reassigned by a subsequent holder.
(b) An assignment shall be filed and recorded and shall be released in the same manner as are liens before judgment.

(c) If notice of the assignment is given as provided by Subchapter E of Chapter 111 of this code, the assignee is fully subrogated to and succeeds to all rights, liens, and remedies of the state.