Hmmm....
I didn't realize you were doing this over a network.
I just tried the same thing over a network:
1) Created a test folder on a Windows Server
2) Added a file into the test folder
3) Created an Outlook email, attached the file, and sent the file to myself.
4) Tried to delete the test FOLDER:
Error Deleting File or Folder
Cannot remove folder "Test Folder": It is being used by another person or program
Close any programs that might be using the file and try again.
Oddly enough, the FILE did delete. But the FOLDER won't delete.
I also tried sending the email to an OUTSIDE mail server. When I did that, I WAS able to delete the test folder.
MORE weirdness:
I created another test folder with files inside. Sent one of the files to myself using Outlook. BEFORE I received the email, I was able to delete the entire test folder.
BUT, when I tried to send another test email, as I was browsing the Server to attach the test file, I got the message:
The folder "\\server\Download\Test Folder" isn't accessible. This folder may be located in an unavailable location, protected with a password, or the filename contains a / or \.
I couldn't navigate to the "\\server\Download" folder until I closed Outlook and restarted Outlook.
Conclusion: You are seeing "Normal" Outlook behavior across the network.
It appears to be a problem with deleting (or moving) a FOLDER across the network, rather than a problem with deleting a FILE. And I think it's only a problem if you send the email internally. If you send the email to an outside mailserver, everything behaves normally.