My spouse and I (married in 2007) am applying for the green card individually, under each one’s employment.

Me: Started GC application in 2006, submitted I485 (years ago), currently working with EAD card.
Spouse: Started GC application in 2005, submitted I485 (6 month ago), currently working with EAD card.

My spouse decided to quit his current job soon, but not sure whether he can get GC before he quits.
In the case he doesn’t get GC AND he cannot find the next job before he quits,

1. Can he stay in the U.S. with his EAD card or my status described above?
2. If yes, please advise any procedures (steps necessary).