That's funny terminolgy, isn't it? Killing a process usually means sending it a signal, typically TERM or KILL, that causes it to exit. But a zombie process is one that has already exited, but hasn't been waited for by its parent, where its parent is either the process that spawned it, or if that process has died, the process with PID 1. This is usually referred to as reaping the zombie process, not killing it. AFAIK, a signal sent to a zombie process is simply ignored.
Or do the quotes around zombie imply a different meaning, such as "zombie-like"?