When using Irssi in Cygterm, it will not close the process and it will remain connected to the IRC server after you close the application.
This happens in Windows 8.1 and I can duplicate the issue at hand. I was connected simultaneously to the same network until it blocked me from access, to discover I had over 5 processes running.
The attached image will show two Irssi.exe processes running but not a single Irssi window open in the taskbar.
irssibot
commented
10 years ago 
When using Irssi in Cygterm, it will not close the process and it will remain connected to the IRC server after you close the application.
This happens in Windows 8.1 and I can duplicate the issue at hand. I was connected simultaneously to the same network until it blocked me from access, to discover I had over 5 processes running.
The attached image will show two Irssi.exe processes running but not a single Irssi window open in the taskbar.
This should not happen.