Reality is that Garrett would have to post 3 years of losing records for Jerry to fire him. Garrett is so connected to Jerry Jones it is pretty much not going to happen while Jerry and Stephen are at the Head of the Dallas Cowboys organization.
Here are some reasons why you are going to be stuck with Garrett for a long long long time:
1. Jerry Jones brought Jason Garrett to be his Tom Landry coach of the Dallas Cowboys.
2. Stephen Jones wanted Jason Garrett to be his Tom Landry coach of the Dallas Cowboys and when Jason Garrett won the last game as interim HC in Philly, Stephen Jones was shown applauding and happy in the press box.
3. Jones is a family business and the Garrett family is family. All of Jim Garretts sons are and have worked in the Dallas Cowboys organization. Jason Garrett's brother Judd is and executive in the Dallas Cowboys front office.
4. Garrett is the only Jimmy Johnson tie loyal to Jerry Jones. When Jerry Jones purged the personnel department (fired Bob Ackles, John Wooten, and Gil Brandt from 1989-1992) to irk Jimmy Johnson, he kept Jim Garrett who had been a scout for the Cowboys since 1987. However, when Tuna came in 2002 he wanted Sean Payton as OC and QB coach because Garrett had no experience at neither position. Because of this Jerry had to wait for the Tuna to leave and his staff contracts expired.
5. Jerry Jones hired Jason Garrett before hiring Son of a Bum as HC and required Philiips to give Garrett the Asst. HC OC position while being paid a higher salary than Phillips the Head Coach.
6. Garrett is a smart connected to the Owner (understands the owner is Head Coach), the Owner's Son and whoever is the Cowboys QB. Jason Garrett bonds with QBs being a former NFL QB. Therefore it is hard to fire a HC you like that is coaching a QB you like. Garrett and Romo were and still are tight. Garrett and Aikman are tight. Romo and the Jones were tight. Garrett and Prescott are tight. Prescott and Jones family are tight (see him QB coach Stephen Jones son). Aikman and Jimmy Johnson are tight. So through Jason Garrett, Jerry Jones can always bring the connection to Jimmy Johnson's Cowboys 90's decade team.
7. Garrett has only one losing season as Head Coach of the Dallas Cowboys during his 7 year tenure. That fits Jerry Jones keep the Cowboys relevant motto.
So Jason Garrett will be fired by Jerry Jones grandson 15-20 years from now.