Oh, I see. In that case, just reopen STDIN, and read from the terminal:

#!/usr/bin/perl -w

use strict;
$| = 1;

my $stream;

while (<>) {
  $stream .= $_;
}

open STDIN, "/dev/tty" or die;

print "Do you want to process the stream? ";
my $ans = <STDIN>;

chomp $ans;
print "Got '$ans'\n";
print "stream = $stream";

#...
exit;
__END__
$ echo foo | ./stdin 
Do you want to process the stream? yes
Got 'yes'
stream = foo
$
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Abigail