After the Jets loss to Denver in the AFC Championship, Leon Hess gave Bill Belichick a $1 million bonus for him to automatically succeed Parcells as the Head Coach of the NYJ. Leon Hess died three months later and the ownership was up in the air. Bill Parcells was know to always let everyone in the dark about his future plans. After the 1999 season, Parcells was thinking about coaching for one more year to honor Leon Hess death (and money, obviously).
When Robert Kraft fired Pete Carroll, Belichick saw the perfect opportunity to be a Head Coach again, with a roster that fit his system (Parcells build that Patriots team) and a stable owner that he had a good relationship. Belichick was tired of chasing Parcells and the Jets new owner (Woody or Dolan) could be a new Art Modell in his life.
So the minute Kraft sent a fax to the Jets requesting to interview Belichick, Bill Parcells quickly stepped down as a HC, triggering Belichick contract, elevating him as the new NYJ Head coach, against his will, and blocking the Patriots attempt to hire him.
The next day, Belichick resigns and a long legal battle started. The NFL ruled in favor of the Jets, who receive a 1st round draft choice in compensation to Belichick signing with the Patriots. Parcells used that pick to trade up for Shaun Ellis and the rest is history...