"inactive" on BPIP is any user with a last active date >90 days ago.
"archived" on BPIP is when a user becomes "inactive"
and has 0 trust, 0 merit, and 0 posts.
Autoban & nuke'd users are also get automatically set to archived when the ban occurs, the "
Geshers" account mentioned in the OP will have both "Archived" & "Banned" status on the site. The extension appears to just display the banned status for those accounts, but any banned account would also get archived.
Once an account is archived, our parsers no longer check the profile. If an archived account makes a post, the parsers would see that and remove the archived status.
In Roy443's case, there was a locked job interfering with the check on recent posts yesterday/today (thanks for the alert!!

), so parsers didn't see those posts, and the account didn't get its "archived" status
removed. The locked job is clear now, but in unique situations like this, anyone can also use "Refresh now" on BPIP's profile page to queue parsers to check the profile and get the status updated for the site & extension.