Why does this have to be done in a single pass? Reading a file backwards is sufficiently awkward that it pays to use a module such as File::ReadBackwards to handle the ugly work for you. I would probably do it something like this:

use strict;
use warnings;
use File::ReadBackwards;

open my $forward, '<', 'filename.txt' or die $!;
while( my $line = <$forward> ) {
    last if $line eq "\n";
}
my $blank_position = tell( $forward );
close $forward;
my $bw = File::ReadBackwards->new( 'filename.txt' ) 
    or die "can't read 'filename.txt' $!" ;

while( defined( my $bw_line = $bw->readline ) ) {
    last if $bw->tell() <= $blank_position;
    print $bw_line;
}
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This is untested, but should give you the general framework.