The main problem I see is, that you are using idiomatic Perl to solve the problem, which makes the solution elegant but requires Perl knowledge to understand the stuff.

I see only one good solution to your problem, which does not change the code, because I see only minor things to change there (in fact, I'd change the die part to something like ... or die "couldn't open output file '$filename' : $!\n".

I would put a comment that describes what each of the idiomatic constructs does, like this :

my ( @results, %fields );

  while(<>){
      # Strip all NULL characters out of the current line
      s/\0//g;

      if (/(?<!from )INSERT INTO Photo/) {
          # Split that line into three parts and save a reference to i
+t
          my @s = ( /([^(]+)(\([^)]+\))(.*)/ );
          push @results, \@s;
      }
  }
  my @final = sort{ $a->[1] cmp $b->[1]  } @results;
  open OUT, ">results.txt" or die $!;
  foreach( @final ) {
      # Print only one occurence of each statement
      my $fieldNames = $_->[1];
      if ( ! exists $fields{ $fieldNames } ) {
          $fields{ $fieldNames } = 1;
          print OUT @{ $_ }
      }
  }
  close OUT;
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This will of course need some learning of Perl on the recipient side, but I think that those comment lines should help the "casual reader" to understand the program flow (if the "casual reader" knows english that is.