The problem is in the title: "line buffered". You're reading P2 line-by-line, but printing only one line total in p2.pl in the first place. Try this in p1.pl: 

#!/usr/bin/perl

use strict;
use warnings;

$|=1;

my $p2 = "./p2.pl";

open(P2,"$p2 |") || die "P2: $p2 - $!\n";
while( read( P2, $_, 1 ) ) { # fixed as per [ikegami]'s post below
    print;
}

[download]

BTW, you should probably be using a lexical filehandle, but given the short example I won't complain too loudly. ;-)

Update: fixed bug in read as pointed out by ikegami in Re^4: Nested line buffered output.

In reply to Re^3: Nested line buffered output by mr_mischief
in thread Nested line buffered output by Anonymous Monk

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