(a) A local government body may not grant extra compensation or extra allowance to a public officer, public employee, or contractor after service has been rendered or a contract has been entered into and performed in whole or in part, or pay a claim under an agreement made without authority of law.

  (b) A city or county, including any chartered city or chartered county, or public district, may not require that its employees be residents of such city, county, or district; except that such employees may be required to reside within a reasonable and specific distance of their place of employment or other designated location.