By default POE traps ctrl-z (SIGTSTP). That's not very handy really. In fact it's quite annoying. It took me a while to figure out how to fix that, so in case anyone else wants to do the same, I created a module for it. Uploading now to CPAN is POE::Component::TSTP.
IRC で聞いたら10分後にはCPANに登録されてました。さすが Matt さん。