In your case, the emails were accessed via POP server. It is primarily meant for emptying the mailbox, the sooner they are received by Outlook.

Yes, they do. I had started just because I wasn't getting complete emails at my Outlook. The way this tool is storing my emails despite deleting them from the server and the Outlook too; I guess, I can save a lot of space in later years by removing them from the server and still having a copy of them.