Since the merger, every single Giants head coach that was fired lost their job in a season in which they failed to beat Philadelphia at least once. With one exception.
One of these coaches was 0-1-1 against Philadelphia in his final season. Two of these coaches were 0-1, instead of the traditional 0-2.
The moral of the story is: If you want to keep your keycard active at 1925 Giants Way, beat the Eagles above all other opponents. Even one win should be enough to guarantee your job.
There have been 14 Head Coaches for the Giants since the Merger. Parcells, of course, was not fired. I'm not sure how many others left on their own volition- or if they were all fired.
Answers: The last coach to beat Philadelphia in his final season before getting fired.
This coach was 0-1-1.
In other words, he is the only non-returning coach who did not lose out to Phila in his final season.