Once a user is removed: 

Direct messages between you and that user will be deleted.

Any group messages including that user will be kept in the chat history.

Action cards that have been assigned to that user will remain assigned to them.

The user's comments will remain on cards.

Projects that are private to the removed user will be deleted from the workspace.

For other projects, you'll get the prompt to reassign them to an active user or keep the removed user as the project owner upon user removal.

If a user is removed from a workspace, their entered time will still remain. This includes Submitted time and estimated time in time tracking.

Timesheet data will remain and be visible in reports. The deleted user will no longer feature in the user filter, you can find their submitted timesheets by adjusting the date range.

If a user has attached a mail thread to an action and they are removed from the workspace, the mail thread will remain visible so long as: 1) the user does not disconnect their email from their Hive account and 2) their email account is still active - i.e. their Gmail/Google account is not deactivated.