It is possible to have this happen on most email systems, but it requires a very odd set-up. Using Outlook, for example, you can set up the 'Advanced' settings to leave a copy of the email on the server. You would then have to have another account reading the same email address but set up not to leave a copy. The first address would then pick up the mail, leaving a copy on the server and the second could then pick it up and delete it.

You are most likely to get into a mess like this if you have set up several accounts for members of your family and something is mistyped.

Of course, you may also have found a completely different way of achieving the same thing.