(a) An assignee may enforce an assignment of rents using one or more of the methods provided by § 64.054 or 64.055 or any other method sufficient to enforce an assignment of rents under a law of this state other than this chapter.
(b) On and after the date on which an assignee begins to enforce an assignment of rents, the assignee is entitled to collect all rents that:
(1) have accrued but remain unpaid on that date; and
(2) accrue on or after that date.