Thank you so much for your reply.
I really don't know how to thank you enough!
This script did exactly what I needed to do.
I modified it a little bit at the end.
Thank you again!

#! usr/bin/perl

opendir(FILES,".")||die "Cannot open files in the directory\n";
@files=();
for(readdir(FILES)){
    if($_=~/\.txt/){
        push(@files, $_);
    }
}
print "@files\n";
for $i(0..$#files){
print "working on $files[$i]\n";
open (FH, "+<$files[$i]") or die "can't update $file: $!";
my $linevalue;
while ( $linevalue = <FH> ) {
    $addr = tell(FH) unless eof(FH);
    last if (eof(FH));
}

if($linevalue =~ /^\s*$/)
{
  truncate(FH, $addr) or die "can't truncate $file: $!";
  print "truncated the last blank line in $files[$i]\n";
}else{
    print "$files[$i] does not end with blank line\n";
}
}
exit;
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