I discovered (more or less) what was happening, by a fluke experience! I have another account at another ISP on which I had never previously checked my mail til today. My user name at the other ISP is just "susan". Now, the likelihood that they've had (in the past) another user named susan is not small. When I executed popclient with user name 'susan' to my alternate ISP, I got a flood of 904 mail messages! Apparently, the ghost-of-susan-past had subscribed to a very active mailing list (majordomo), and then never unsubscribed.
This gave an opportunity to check where the messages were going: popclient calls sendmail. The messages being received seem to go first into /var/spool/mqueue. Then the messages go from there to ~/var/mailagent/queue. Since the last line of my ~/.rules file is "{ SAVE +inbox };", files that don't match any preceding rules go from ~/var/mailagent/queue to +inbox. Apparently, mailagent doesn't finish dumping its queue (either to mbox.username or to +inbox) before it lets the user start reading the results. I don't know if this is the planned procedure, but it seems both inefficient (3 boxes for each message) and confusing (the user isn't notified when mailagent is finished its work). Sorry for using so much bandwidth over this problem; I hope some of it is useful to somebody. Susan Kleinmann