undef $old;

$old = {
         'child' => {
                      'parent' => $old,  # !!!
                      'name' => 'bob jr'
                    },
         'name' => 'bob'
       };
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Obviously, the parent key is assigned the new value of $old, which is, well, undef.

Update: You want to check the Data::Dumper POD for the $Data::Dumper::Purity setting.

#!/usr/bin/perl -w
use strict;
use Data::Dumper;

my $old = {
    name => "bob",
    child => {
        name => "bob jr",
    }
};
$old->{child}{parent} = $old;

$Data::Dumper::Purity = 1;
print Data::Dumper->Dump([$old], ['$old']);

__END__
$old = {
         'child' => {
                      'parent' => {},
                      'name' => 'bob jr'
                    },
         'name' => 'bob'
       };
$old->{'child'}{'parent'} = $old;
[download]

Makeshifts last the longest.