Here, in the Test::More format that may, in future, avoid a great deal of confusion, is a possible solution based on ikegami's solution. Note that the  => (fat comma) in an expression like
    [ 'leftrightabc' => 'left', 'rightabc' ],
is just a notational indulgence that is intended to be read as "produces" or "yields" and that is syntactically just a plain old  , (comma) (update: because its LHS is fully quoted).

c:\@Work\Perl\monks>perl -wMstrict -le
"use Test::More 'no_plan';
 use Test::NoWarnings;
 ;;
 use constant TEST_1 => (
  [ 'left'         => 'left', ''         ],
  [ 'right'        => '',     'right'    ],
  [ 'rightabc'     => '',     'rightabc' ],
  [ 'leftright'    => 'left', 'right'    ],
  [ 'leftrightabc' => 'left', 'rightabc' ],
  );
 ;;
 my $specific_string = qr{ right }xms;
 ;;
 my $right_side = qr{ $specific_string .* \z  }xms;
 my $left_side  = qr{ (?! $specific_string) . }xms;
 ;;
 VECTOR:
 for my $ar_vector (TEST_1) {
   my ($string, @expected) = @$ar_vector;
   ;;
   is_deeply [ $string =~ m{ \A ($left_side*) ($right_side?) }xms ],
             \@expected,
             qq{'$string' -> '$expected[0]' '$expected[1]'};
   }
 ;;
 done_testing;
"
ok 1 - 'left' -> 'left' ''
ok 2 - 'right' -> '' 'right'
ok 3 - 'rightabc' -> '' 'rightabc'
ok 4 - 'leftright' -> 'left' 'right'
ok 5 - 'leftrightabc' -> 'left' 'rightabc'
1..5
ok 6 - no warnings
1..6
[download]

Update: Note also that  $specific_string could be any  qr// pattern.