In a fixed-term employment contract, the end of the employment is set clearly at the very start. Upon the expiration date, your employment relations with the employer ends automatically- so no extra move is required. A permanent employment contract, on the other hand, does not include and end date. Therefore, your permanent employment contract will not stop unless you or your employer actively terminate it.
Please note: If you are not sure whether you will find a new job after the end of your fixed-term contract, you must notify the Employment Agency at least three months before the end of your contract. Otherwise, you risk cuts in your unemployment benefits.