I apologize, as taking way too much of your time. Please know that I appreciate your help! Updated code appears below.

#! /usr/bin/perl -w
use strict;
use warnings;
use lib "c:/strawberry/perl/site/lib";
use open ':std', ':encoding(UTF-8)';

#Specify location of input files;
my $files_dir = 'D:/research/audit fee models/filings/test';

#Specify location of output results;
my $write_dir = 'D:/research/audit fee models/filings/filenames/filena
+mes.txt'

#Open the directory containing the input files you will loop through;
opendir (my $dir_handle, $files_dir);

#Set up a loop for the sequentially reading the input files;
while (my $filename = readdir($dir_handle))   {
  
  next unless -f $files_dir.'/'.$filename;
  print "Procesing $filename\n";

#Open the next file in the directory; 
  open my $fh_in, '<', $files_dir.'/'.$filename
      or die "failed to open '$filename' for read";


   
#Initialize file counter;
  my $count=0; 
  
#Establish a loop to read the open file line by line;
  while (my $line = <$fh_in>) {     #begin WHILE loop;
   print $line;
      
#Open the output file for saving the results;  
  open my $fh_out, '>', $write_dir.'/'.$filename
      or die "failed to open '$filename' for write";
      
       print $fh_out "$line\n";   #write results to file;
         
        ++$count;    #update line counter;
    
                              }   #end of while loop for current line;
     
   print "$count lines read from $filename\n;"  
   
 }  #end of current file loop;
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