Chinese passports, family-declaration forms, and a closed departure gate — the image the new workplace sweep is meant to produce.

A day before new nationwide exit-entry rules take effect, people inside China’s state system say their workplaces have already widened a quieter campaign: employees at government offices, state banks, state-owned firms, public hospitals and schools are being told to declare not only their own passports, but those of their families — including foreign passports and overseas residence papers.