You forgot to declare some variables:). Fixed:

#!/usr/bin/perl

use strict;
use warnings;
use MIME::Parser;

sub parse {
    use MIME::Parser;
    my $dir = 'c:\\tmp\\parsedemails';
    if ( not -d $dir ) {
         die "Can't create directory ${dir}: $!\n"
         unless mkdir $dir;
    }
    
    my $fileopen;
    my $parser = new MIME::Parser;
    $parser->output_under($dir);
    die "Can't read ${fileopen}: $!\n" 
    unless open my $fh , '<', $fileopen;

    my $entity = $parser->parse($fh);
    my $path = "c:\\tmp\\parsedemails";
    opendir DIR, $path;
    
    my @lines = readdir(DIR);
    closedir DIR;
    
    my @files;    
    my $directory = $lines[$#lines];
    print "DIR  $directory END ";
    my $pathdir = $path . "\\" . $directory;
    die "Can't opendir ${pathdir}: $!"
    unless opendir DIR, $pathdir;
    while (defined( my $file = readdir DIR )) {
        push @files, $file;
    }
    closedir DIR;
}
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