It seems that sent messages stay in the inbox of inactive users. When I check Sent Messages I can see a list of messages sent to Chingy way back in 2008. These messages haven't been deleted by the user and seem to stay like that. In the future as some users become inactive the list might get bigger and bigger.
I have so many noobish PM's incoming from members that are destined to get banned. So there is no surprise for mine to look so long.
I don't see any harm in having them there, it doesn't count towards your PM box limit as far as I know.
(Mine is probably a majority of banned users, as the warnings show up in there : P)
All times are (GMT -06:00) Central Time (US & Canada). Current time is 9:11:30 PM