Short synopsis:  quota almost reached.  On the web host, sent box almost full (925 mb);  Set up an imap account on desktop computer, downloaded sent, moved sent to local: sent;  waited a few days, checked webmail host:  sent shows 0 messages, 925 MB used.  Inbox: 4 meg, drafts: 0, junk: 0, trash: 1mb, shaw-restored-jul11-2016:0 (just to be complete... that one has been empty since then).  BUT:  sent:(messages:0;size: 925mb) with properties: no retention policy set.
I can't get the sent to reset its size.  There is nowhere in the GUI that I can find to do that.  Clearly the system is not resetting the size for me.  I spent an hour back and forth, starting with a chat bot, then a dude who will remain nameless who's final statement to me was:  "I tried deleting emails from my account and it works just fine", this after an hour of getting, first, the robot, then him to take the point seriously and solve the issue.  CLEARLY these guys know nothing about the mail server.  So I am off to the community in the hope that someone will have a clue.
 
Thanks in advance for any help on this.