I recommend using a piping form of open, and capturing the returned PID. Then, in your signal handler, you can kill the PID, to ensure it goes away. Example:

    my $pid;

    eval {
        local $SIG{ALRM} = sub { die "TIMEOUT" };
        alarm 2;
        $pid = open my $fh, "sleep 30|";
        alarm 0;
    }

    if ($@ eq "TIMEOUT") {
        print "kill $pid\n";
        kill 1, $pid;
    } elsif ($@) {
        die $@;
    }
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Take note that your example code had an error -- the key in %SIG should be ALRM and not ALARM.

Update: apparently Joost posted essentially the same answer, but 10 minutes earlier than I did. Oh well, I guess that can be seen as validation of some sort.

Update: fixed silly syntax error