No offense but this doesn't really sound like a problem with the module. The truth is you should be managing your disk space properly. Look into Nagios it will monitor disk space (among many other things) for you.

Looking at current source, I see a die when file can not be written, so I assume you are evaling the Proc::PID::File->running() call and disregarding the result. But I can't tell for certain because you didn't post any code. It does die for me when I try to assign it to my CD.

IIRC, you can also clear your program's pid files at the beginning of reboot in rc.sysinit

UPDATE:
Since our data changes a lot, the slave quickly filled up the disk. I don't think monitoring tools would have avoided me waking up to a thrashing box.

Sure it could - I've written many Nagios Plugins. All of them before helpful modules like Nagios::Plugin. Writing Nagios plugin are not difficult, that's why I like it. You could easily monitor the number of file to be processed. Not to mention that Nagios also has CPU and Memory (and IIRC swapping monitors) already built in.