package MyModule;

sub STORABLE_freeze {
  my $this = shift;
  my $value = $this->{'key'};
  delete $this->{'key'};
  my $serialized = $this->SUPER::STORABLE_freeze( @_ );
    # or $this->SUPER::freeze( @_ ) or etc. etc.
  $this->{'key'} = $key;
  return $serialized;
}

sub STORABLE_thaw {
  my $this = shift;
  $this->SUPER::STORABLE_thaw( @_ );
    # or $this->SUPER::thaw( @_ ) or any other arrangment
  $this->post_loaded_function();
}

1;