Here is my first attempt. For testing, I use perl -wpe 1 as external program, which acts as "poor man's cat":

use strict;
use warnings;
use IPC::Open2;
$|=1;
$SIG{PIPE} = sub { print STDERR "SIGPIPE received\n"; exit; };
my $pid = open2(my $reader, my $writer, 'perl -wpe 1');
print $writer "$_\n" for (qw(first second third));
print "Data written\n";
close $writer;
print "Reading from pipe:\n";
while(my $data=<$reader>) {
    print "Received: ".<$reader>."\n";
}
close $reader;
print "No more data\n";
waitpid($pid, 0);
print "Finished\n";
[download]

Data written
Reading from pipe:
[download]

and then hangs. Obviously, reading from the pipe does not work. Indeed, I found the following warning in IPC::Open2]: