There are a variety of tasks that might need to be completed - closing a case, the re-verification of eligibility for someone whose documents are expiring, etc.
Why not email a reminder that there is something to be done? I have employees with documents that don't expire until 2019. Ok, hang on a second, let me flip my calendar to seven years hence and mark on it to re-check their documents. If I am not here, since we have a corporate account, the reminder could go to the administrator. It doesn't even have to say "Hey, check so-and-so's documents". It can just say "You have an e-verify reminder".