What happens at UAL, DAL or AA (or any other major for that matter) if you are delayed and needed to fly into the 2 hour extension of your FDP?

Are you automatically extended? Is there any pay benefit for doing so?

My employer says you automatically agree to the extension when you sign the "fit for duty" paperwork before each leg. If you are delayed and refuse the extension, my work considers it a Fatigue call. Also, it my trigger a strike against you in our "dependability policy" where you may be disciplined. This also my lead to the loss of pay.

Thanks.