No, the problem is that $k is not available (slightly different than garbage collected). It is included in the closure, as this demonstrates:

use strict;
use warnings;

$::clos = $::clos = "global";

sub foo {
   my $clos = shift;
   my $sub = shift;
   &$sub() if $sub;
   return sub {
      eval 'print "$clos\n"'
   }
}

foo("baz", foo("bar"));
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The first (inside) call to foo returns a closure on foo's $clos. The second call to foo calls the closure, which does get the closed-over $clos. But there is a problem: entering foo the second time reuses the same lexical $clos, since perl isn't aware that the first call will be referring to it, so as an optimization doesn't bother allocating a new lexical.

Note that in 5.10.0, the OP's problem code gives a warning:

Variable "$k" is not available at (eval 1) line 1.
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