If a closure is "a special case of an anonymous subroutine holding onto data that used to belong to its scope at the time of its creation" (S.Srinivasan in Advanced Perl Programming), then your code is behaving right, although strict has failed to detect that $x within the anonymous sub isn't referring to the same $x within the grand-parent scope.

However, having said that, though anonymous subroutines are oblivious to lexicals in a grand-parent scope, normal subroutines aren't, also a normal subroutine might not derive and use a set of parent lexicals but its "children" subroutines might do, so the characteristic is intranstive, consider the following..

sub test_sub {
    print &{+shift};
}

{
  my $x = "hello";
  my $y = "world";
  local $, = " : ";

  print "x - local lexical1 : $x ", \$x;
  print "y - local lexical1 : $y ", \$y;
  sub foo {
    test_sub( sub { "x - derived lexical (anon) : $x ", \$x } );
    print "y - derived lexical (foo) : $y ", \$y;
    test_sub( sub { "y - derived lexical (anon) : $y ", \$y } );
    sub bar {
        sub baz {
            print "x - derived lexical (baz) : $x ", \$x;
        }
    }
  }
  print "x - local lexical2 : $x ", \$x;
  print "y - local lexical2 : $y ", \$y;
}

foo();
baz();

__END__

__output__

x - local lexical1 : hello  : SCALAR(0x814c630)
y - local lexical1 : world  : SCALAR(0x814c6f0)
x - local lexical2 : hello  : SCALAR(0x814c630)
y - local lexical2 : world  : SCALAR(0x814c6f0)
Use of uninitialized value in concatenation (.) or string at foo line 
+17.
x - derived lexical (anon) :  SCALAR(0x814bc28)
y - derived lexical (foo) : world SCALAR(0x814c6f0)
y - derived lexical (anon) : world SCALAR(0x814c6f0)
x - derived lexical (baz) : hello SCALAR(0x814c630)
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Notice, that within foo() \$x refers to a different location than \$x in the parent scope.

To better redefine a closure: "A closure is an anonymous subroutine accessing the immediate local scope at the time of its creation" (atleast for <= perl 5.8.x). So, it might be better to ensure that all lexicals needed to be squirreled away by a closure are explicitly typed within the immediate local scope.