For instance, how do you write a test that tests your objects ... timely destruct?

How about (untested):

  {
    package CrashDummy;
    @CrashDummy::ISA = 'MyPrecious';
    *ok = \&Test::More::ok;
    my $counter = 0;
    sub DESTROY {
      Test::More::ok( ++$counter == 2, 'DESTROY called' );
      $_[ 0 ]->SUPER::DESTROY;
    }
    {
      my $dummy = bless +{}, __PACKAGE__;
      ok( ++$counter == 1, 'inner scope' );
    }
    ok( ++$counter == 3, 'expected execution order' );
  }
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?

How do you test your shuffling or die rolling technique is fair and produces results according to your specifications (say, according to a Gaussing distribution), and isn't biased favouring certain outcomes?

There are a bazillion statistical tests to compare sampled distributions. I'm surprised none of these would meet your needs.