The details of contracts vary from airline to airline. However there are two elements in common.
1. There are regulatory maximums that cannot be exceeded. This is complex, depending on a variety of factors such as when you started and how many legs you have. Contracts cannot override these. this is referred to as timing out.
2. Any pilot may call fatigued at any time and MUST be removed from the flight assignment. The pilot cannot be punished for this action.

This is because, as others have stated, pilot fatigue is frequently the leading cause of aircraft accidents. As inconvenient as it may be for you to have your flight cancel, it's better than dying.

At my airline, using the word fatigue with crew control is all you need to do for them to start looking for a replacement. All fatigue calls require a follow up report that is reviewed. If you made every effort to be rested and the fatigue was not your fault, you will be paid for the cancelled flight. The airline and the FAA does not want us flying tired. Not should you.

In my experience, pilots are mindful of the disruption caused and do not take a fatigue call lightly.

Timing out is not in the pilots hands. And, you must be able to complete the flight before timing out which is why timeouts usual happen at the departure airport, often on taxi out or after boarding when it becomes apparent that due to delays, the flight cannot be completed.

Hope this helps clarify the rules.