Is it just me, or does anyone else think there should be an internet convention where, when one person leaves in the middle of PM exchanges, the other person is alerted?

The internet has acronyms for everything. Am I the only one that thinks there should be a convention adopted so that when you’re exchanging PM’s with someone, and that person leaves, there’s some sort of “Good Bye” to let the other person know? Am I the only one who sits and waits (and waits) for the response that never comes? To be honest, I’m just as guilty. But it wastes SO MUCH time. Sure there are things that pull people away quickly (like the boss coming by) but maybe it’s something that could be done automatically by the ISP or the site? What do you think?