It depends on valid status and appropriate evidence, not the private project end date. Read the spouse’s own immigration records.
Keep family permission separate from delivery milestones
A qualifying L spouse may work incident to valid status. Children do not receive that benefit and must remain eligible unmarried children under 21. A project extension does not itself extend anyone’s authorized stay.
Record each family member's intended work or study plan and relevant dates, and confirm the spouse's actual documentation rather than assuming identical treatment regardless of category. Households that have moved between assignments usually hold a scattered set of documents across several countries, and the practical advice is to consolidate them before they are needed: each family member's passports including expired ones, birth certificates, school records and any prior immigration documents. Where a family previously moved together, the questions worth re-asking are narrow: has any child married or turned 21, does any family member now hold a different status, and has any document been superseded by later travel. Each family member holds whatever status was actually granted to that person, with its own validity period and its own permitted activities; nothing is inherited from the principal’s travel pattern.