Patients' Right to Fair Compensation and Protection Against Predatory Contingency Fee Practices Act - Prohibits an attorney from entering into or enforcing a contract, whether express or implied, for attorney fees in connection with a health care liability action to the extent that the amount or payment of such fees is: (1) contingent upon the resolution of the action; and (2) in excess of the specified maximum allowed percentage (ten percent of the amount recovered by the claimant in connection with the action, subject to exception).