#!/usr/bin/perl

use strict;
use warnings;

$|=1;

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

open(P2,"$p2 |") || die "P2: $p2 - $!\n";
while(<P2>) {
   print;
}
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#!/usr/bin/perl

use strict;
use warnings;
$|=1;

my $i;

for $i (1..10) {
   print ".";
   sleep 1;
}
print "\n";
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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;
}
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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.

The fourth arg of read is wrong. It should be 0 or simply omitted.

If you're going to read one character at a time, getc would be clearer. But I recommend reading all available data instead of one character at a time. You can do that using sysread since it returns all available data (up to the specified limit) as soon as any data is available.