A quick question:
Is $socket really an IO::Socket::INET object or is it the result of the accept method?

I did a simple test script:

#!/usr/local/bin/perl -w
use strict;
use IO::Socket;

my $sock = IO::Socket::INET->new(
                                 Proto => 'tcp',
                                 LocalPort => 8080,
                                 Listen    => SOMAXCONN,
                                 Reuse     => 1
                                );

my $data = 'Silly test string.';

{
    local $\ = qq(\0);
    print $sock $data || die "What happened? $!";

}
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..and this executes just fine, no warnings, no errors. Did I mention that there's no client on the other end?

If you don't make $socket like this (set your ports and such however):

$inet = IO::Socket::INET->new(
                              Proto => 'tcp',
                              LocalPort => 8080,
                              Listen    => SOMAXCONN,
                              Reuse     => 1
                             );
$socket = $inet->accept();
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then it's entirely possible that you never talk to your client properly at all. The fact that it exits as though it sees a null byte may simply be a timeout exit.

Just a thought -- I'm no socket guru :)