When performing the "Mail Archiving" operation, currently the user is issued a warning "Fetching new mail will remove them from the server!" and the emails are deleted from the server after mail archiving.
The users should be given an option by which, if they desire, they can leave a copy of the emails on the server instead of deleting it from there after mail archiving.
Attached a screenshot of the warning message currently issued during Email Archiving.