Barbra Streisand might not brim with the white-hot cultural relevance she used to, but nobody can deny that she’s a trier. For example, when everyone’s back was turned, she went off and created her very own Black Mirror episode.

In her episode, a broken-hearted millionaire realises that she cannot bear to part with her sick dog, so she spends an inordinate amount of money to have it cloned. However, with every passing day, the millionaire realises the futility of her gesture. The clones don’t behave like the original, and the differences between old and new tear at her soul until she drowns the puppies in a lake.

Apart from the last part (it wouldn’t be Black Mirror unless it ended on a note of harrowing violence) this has all actually happened. In a recent Variety interview, Streisand revealed that her Coton de Tulear dogs, Miss Violet and Miss Scarlett, were created in a lab. She had them made, at great expense, from genetic material taken from her dog Samantha, who died last year.

Tragically, she now hints that it might have been a mistake. The new dogs might look like Samantha, but don’t behave like her. “I’m waiting for them to get older so I can see if they have her brown eyes and her seriousness,” she said.

Without sounding too solipsistic, a big part of owning a pet is to learn about death. You take custody of an animal knowing that you’re likely to outlive it. While it’s alive you swaddle it in as much love as you possibly can, and then it dies, and then you’re bereft, and then, slowly, you learn how to move on. Little by little, pets equip you with the tools to deal with grief.

‘Barbra Streisand refused to let go.’ Photograph: KMazur/WireImage

I vividly remember the day my first pet died – a guinea pig called Smartie. My mum met me at the school gates and told me that Smartie had passed away that morning. She told me that it wasn’t anyone’s fault, and that I’d feel sad for a while, but the sadness would eventually fade. It would hurt, but it would be OK.

I remember grappling with the enormity of the information. I was six, after all, and this was my first experience of death. But I’m pleased it happened. It’s something that everyone needs to go through. Had my mum met me at the school gates with a bubble-wrapped Smartie clone, and explained that there’s no such thing as death so long as a South Korean laboratory continues to churn out exact genetic reproductions of everything you’ve ever loved at tens of thousands of pounds a pop, you can understand how it might have skewed my understanding of mortality a little.

And that’s the saddest part of this Barbra Streisand news. It isn’t that the clones were expensive and that her money would have been better going to charity. It isn’t that she paid for them at all, rather than adopting a couple of strays from a shelter. It’s that she refused to let go. She failed to grasp the most fundamental point of life: it ends. And once it’s over, you can never get it back. Nothing – not prayer, not magic, not science – can replace what was gone. You can come close, but it’ll never quite be the same. Some things you just can’t run from.

• Stuart Heritage is a Guardian columnist