Yes, it’s possible to stay in F-1 status while your green card is pending as long as you keep meeting all F-1 requirements (like full-time study).

Once you file I-485, you're allowed to stay in the U.S. under a status called “authorized stay” while the green card is pending.

You can file for adjustment of status (Form I-485) from within the U.S. and stay here while your application is pending even if your F-1 status later expires.

 If your F-1 status ends e.g., you graduate or stop studying, you’ll still be in legal status if your I-485 is pending.