An H-4 dependent spouse or child is in status only while the H-1B is in status. H-4 dependents are not eligible for any employment authorization. An H-4 dependent who works is out of status even though the H-1B may still be in status.
H-4 dependent’s extensions should normally be filed at the same time as the H-1B. At the time of the principal’s extension a separate form I-539 should be submitted for H-4 family members.