Dependants' status generally ends with the principal's. A spouse's employment authorization stops with it, and a child who has turned twenty-one has already lost derivative status independently.
Two clocks, and the child's runs out first
Hypothetical example: the technologist has three years of the limit remaining, his wife works locally in dependent status, and their son is seventeen. The son's derivative status ends on his twenty-first birthday, which falls before the principal's limit does, so his own route — a student status or something else on his own facts — has to be arranged separately and well in advance. The wife may work while the principal holds valid status, because authorization is incident to that status, but it does not survive the end of it.
Families in the final year of a capped assignment therefore need a decision rather than a hope: a different category, a permanent route begun early enough to be useful, or a planned departure. The uncomfortable version of this conversation happens in the eleventh month.