The parent is notified of which signal killed a child. If you wanted to monitor that, you could write a wrapper.

use IPC::Open3 qw( open3 );

my $child_pid = open3(
   '<&STDIN',
   '>&STDOUT',
   *CHILD_ERROR,
   @ARGV
);

my $error = '';
1 while read(CHILD_ERROR, $error, 64*1024, length($error));

$error .= "\n"
   if length($error) && substr($error, -1) ne "\n";

waitpid($child_pid, 0);

my $code = 0;
if ($? & 0x7F) {
   $error .= "Child killed by signal ".( $? & 0x7F )."\n";
   $code = 0x80 | $?;
}
elsif ($? >> 8) {
   $error .= "Child exited with error ".( $? >> 8 )."\n";
   $code = $? >> 8;
}

if (length($error)) {
   # Email $error here.
}

exit($code);
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(As you can see, you no longer need custom handlers for warnings and exceptions in the script itself, unless you want to add stack backtraces.)