I tried to come up with a solution using tr/// since its much faster, but had to bring in the s/// operator instead...

#!/usr/bin/perl -wT
use strict;
no warnings "uninitialized";  # printing undef triggers a stupid warni
+ng

# testing loop
for my $pair (['aabbcc',   'abc'],
              ['aabbccdd', 'abcdd'],
              ['abc',      'abc'],
              ['abc',      '123'],
             ) {
  my $left = leftover(@$pair);
  printf ("%8s - %-6s => %-5s\n",@$pair,"'$left'");
}

# scrabble "subtraction" subroutine
sub leftover {
  my $string  = shift;
  my $letters = shift;
  $string =~ s/$_// || return for split // => $letters;
  return $string;
}

=OUTPUT
  aabbcc - abc   => 'abc'
aabbccdd - abcdd => 'abc'
     abc - abc   => ''
     abc - 123   => ''
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You'll have to be careful in your usage of this sub, since your specs state nearly opposite meanings for the return values of '' and undef.

Update: added || return to test for unmatched chars.

-Blake