Following on from @Journetman Geek 's answer, what you are talking about is indeed a bouncer. But even in a free shell that does not provide a bouncer, you can still stay online with your nick even if you are not actually logged into the shell. The trick is to use
Start up a
screen session and start irssi from within it. Then, when you want to log out, don't /quit from irssi but deattach from screen (use
C-a d) and then logout of the shell. When you login back into the shell again, just start screen to reattach to the running session (use
screen -raAd). Thus your nick stays online even though you are off the shell.