drocha the usual behavior for an IMAP mail account is to store its sent mail in an IMAP mail folder on the server.
Since the mail is stored on the server, if you remove that account you will no longer have access to that server and those lose access to those sent messages.
If that's not the behavior you want then edit your mail account preferences to change the location of sent mail to a local folder on your computer. In Apple Mail, you can do that via Preferences > Accounts > (select the account) > Mailbox Behaviors.
I assume Outlook has similar options, so check your account settings there and look for them.
Hope this helps 🙂