Someone from your Steam friend list did send you a message and removed you from the friend list later and there is now an unread message symbol that won’t go away? You do now see an unread message symbol and if you click on it, you will see a chat window of an unknown person in Steam. This is annoying but you can fix the issue and here is how…

Click on the drop down menu of the unknown and block this person. Then log out of Steam and log back in. Now click again on the unread message symbol and unblock the person. Problem should now be solved and there is no longer an unread message of an unknown person. This should have fixed your issue.