Dependants may study and may not work, for the whole period and not merely at the start. Their status ends when the principal's does. Dependent status also requires each child to be unmarried and under twenty-one, so a sixteen-year-old has a fixed horizon that no renewal extends.
The permissions never widen on their own
Households sometimes assume that dependent restrictions soften with time, that a spouse who has lived in a community for three years acquires some entitlement to work there, or that a long-settled teenager can take a part-time job like their classmates. Neither is so. The prohibition on employment for dependants in this category applies throughout, and it does not distinguish between a career position and casual weekend work.
Schooling, by contrast, is permitted at any level. The condition that most often forces a change is age. Dependent status requires the child to be unmarried and under twenty-one, and the birthday arrives regardless of how well the family is settled, so a household with a sixteen-year-old should be planning a transition to student status in the right academic year rather than in the month it becomes urgent.
A spouse who wants to work needs her own basis, and that is a project with its own timeline.