You can stay in the US while your appeal is pending with the Administrative Appeals Office (AAO) or the Board of Immigration Appeals (BIA).

If you have a valid nonimmigrant status (e.g., H-1B, F-1), you can maintain your stay in the US until its expiration or until you depart.

If you have an approved EAD (Form I-766) based on a pending green card application, you might be able to stay and work in the US until its expiration.