Killing processes that don't want to die

Suppose you have a program running on your system that you don't quite trust. Maybe it's a program submitted by a student to an automated grading system. Or maybe it's a QEMU device model running in a Xen control domain ("domain 0" or "dom0"), and you want to make sure that even if an attacker from a rogue virtual machine manages to take over the QEMU process, they can't do any further harm. There are many things you want to do as far as restricting its ability to do mischief. But one thing in particular you probably want to do is to be able to reliably kill the process once you think it should be done. This turns out to be quite a bit more tricky than you'd think.