回复：让你原单位(档案所在地)出个证明，然后去公证处公证一下

A friend has helped me to ask all around. The police station that has my HuKou imposes this requirement—although not all police stations do that.
No company of mine likes to do what you suggested—especially since I left four years ago—almost all my colleagues have left that company. Moreover, the police does not care about that.