while ( my $html_file = $rule->match ) {
   # Change file in-place.
   local @ARGV = $html_file; 	
   local $^I = '.bak';  # Or '' to avoid making backups.

   while (<>) {
      ...

      # Keep (possibly edited) line
      print;
   }
}

##</code><code>##

while ( my $html_file = $rule->match ) {
   rename($html_file, "$html_file.bak")    or die;
   open(my $fh_in,  '<', "$html_file.bak") or die;
   open(my $fh_out, '>', $html_file)       or die;

   while (<$fh_in>) {
      ...

      # Keep (possibly edited) line
      print $fh_in $_;
   }
}