How to Kill a Defunct Process Whose Parent is Init

By default, no, that's not allowed. Under Linux (from man 2 kill):

The only signals that can be sent to process ID 1, the init process, are those for which init has explicitly installed signal handlers. This is done to assure the system is not brought down accidentally.

Pid 1 (init) can decide to allow itself to be killed, in which case the "kill" is basically a request for it to shut itself down. This is one possible way to implement the halt command, though I'm not aware of any init that does that.

On a Mac, killing launchd (its init analogue) with signal 15 (SIGTERM) will immediately reboot the system, without bothering to shut down running programs cleanly. Killing it with the uncatchable signal 9 (SIGKILL) does nothing, showing that Mac's kill() semantics are the same as Linux's in this respect.

At the moment, I don't have a Linux box handy that I'm willing to experiment with, so the question of what Linux's init does with a SIGTERM will have to wait. And with init replacement projects like Upstart and Systemd being popular these days, the answer could be variable.

UPDATE: On Linux, init explicitly ignores SIGTERM, so it does nothing. @jsbillings has information on what Upstart and Systemd do.

You can either have your cake or eat it. The program wants to have as long as it needs (or wants) to react to SIGTERM. The system (program manager) wants to be able to terminate. If the system waits forever, this allows a program to hijack system shutdown by never responding (either because the program is malicious or because it is buggy).

In a normal shutdown sequence, each daemon is terminated via an init script (call it a shutdown script if you want) provided by the author or the packager of the daemon. Depending on the daemon, the init script may just send it a signal, or it may do a more controlled shutdown (e.g. by writing to a socket). The init script may wait for the daemon to report that it has satisfactorily shut down, or it may forcibly kill it. Init scripts run as root (they may call su to perform part of their task as a less privileged user); they are supposed to be cooperative, so they're allowed to leave the system hanging forever.

Once init scripts have finished their job, all services are supposed to be shut down. Any remaining process is supposed to be either unimportant or misbehaving. So at this stage the remaining processes get told to shut down (SIGTERM), and after a grace period (giving them a last chance to shut down cleanly) the system must go down so any remaining processes are killed forcibly (SIGKILL).

Think of the init scripts as the normal arrest procedure — show warrants, shout a warning, etc. A law-abiding daemon should shut down at this point, though daemons have lawyers (the init scripts) that can delay the procedure as long as they want. Once the normal process is finished, remaining daemons are presumed hostile. The system fires a warning shot (SIGTERM), then after a delay shoots to SIGKILL.