Ideas gushed from Robert Louis Stevenson like water out of the Trevi Fountain. The number of books envisaged by him far exceeded the number he would ever have been able to complete. There were plays, histories, collections of stories, memoirs and many novels that were either stillborn or expired in infancy. One such was ‘The Shovels of Newton French’ – not the snappiest of RLS’s titles – about a highwayman hanged for murdering a policeman. Another destined not to survive was provisionally called ‘What was on the Slate’, which he hoped to co-author with his wife, Fanny. Once it was given a new title and a different denouement, Stevenson told W E Henley, the model for Long John Silver, it was ‘going to shoot up and become a star’. Alas, it fizzled out like a cheap firework, as many of his projects had a tendency to do.

As his biographer Claire Harman has noted, he was a serial offender when it came to boasting about books in the pipeline. She reckoned that there were enough aborted efforts to furnish two or three further careers. ‘With a little push this way or that, Stevenson might not have been known as the author of Treasure Island and Dr Jekyll and Mr Hyde but as the playwright of The King’s Rubies, or the biographer of Viscount Dundee.’

Some of his projects got nearer to completion than others. At his death in Samoa in 1894, at the age of forty-four, he left two novels, St Ives and Weir of Hermiston, in a state of suspended animation. It is his failure to complete the latter that is the bigger source of regret. Published in 1896, it was hailed by Arnold Bennett as a masterpiece and deemed a greater achievement than anything that had preceded it. That was an eccentric judgement. The novel ends mid-sentence with the phrase ‘a wilful convulsion of brute nature’, words that might be applied to the cerebral haemorrhage that killed Stevenson. His friend Sidney Colvin, introducing Weir of Hermiston to its first readers, wrote, ‘Surely no son of Scotland has died leaving with his last breath a worthier tribute to the land he loved.’

Weir of Hermiston, as Colvin acknowledged, is to Stevenson’s oeuvre what The Mystery of Edwin Drood is to Dickens’s. Reading reviews of both novels, one is struck by the desire to protect and promote them, the incompleteness a sign of vulnerability and fragility. It is as if by leaving them bereft of endings, their authors have somehow been negligent, like harassed parents who leave a child behind in a supermarket. Edwin Drood, which was unfinished by Dickens on his death 150 years ago, has puzzled readers ever since and several writers have tried to resolve the mystery at its core. Such attempts deserve admiration, but the results are inevitably unsatisfactory, not least because Dickens is inimitable. You might be able to mimic his style for a few pages – see Robert Benchley’s delightful parody of A Christmas Carol – but it’s not sustainable for much longer.

It is perhaps best to be thankful for what we have and let well alone. Must we have an ending to Jane Austen’s Sanditon? It seems we must. The first to attempt one was Anna Austen Lefroy, the novelist’s niece, but it defeated her. More recently, Andrew Davies freely adapted it for ITV, in the process enraging Austen’s devotees with a steamy scene, redolent of those on Love Island, between two of the principal characters. Janeites were not amused.

My favourite unfinished novel is F Scott Fitzgerald’s The Last Tycoon. Like Stevenson, Fitzgerald did not enjoy good health; he too was forty-four when he died. His original intention was to write a novel of around sixty thousand words but by the time of his death he was boasting that he had achieved seventy thousand and was little more than halfway through the story. Even in its fragmentary form, it was, opined Edmund Wilson, its author’s ‘most mature piece of work’.

The novel is set in Hollywood; the titular tycoon, Monroe Stahr, was based on the movie mogul Irving Thalberg. My Penguin edition includes thirty-five pages of Fitzgerald’s notes and aphorisms, among which is the endlessly repeated aperçu, ‘There are no second acts in American lives.’ This could, of course, be read as Fitzgerald’s own epitaph. No one now doubts the genius of The Great Gatsby but his other completed books have mostly struggled to thrive under the unforgiving microscope of posterity.

If completed, The Last Tycoon might have revivified his reputation, which in the 1930s had crashed like the American economy. His letters to his wife, Zelda, acknowledge that he had ground to make up. Indeed, he thought it might be his valedictory novel ‘because, after fifty, one is different’. He made that pronouncement in October 1940, when on a good day he was writing two thousand words. A month later, however, he was toiling: ‘The novel is hard as pulling teeth but that is because it is in its early character-planting phase.’ By 6 December, he was having ‘trouble’ with his heart and tiring quickly: ‘No news except that the novel progresses and I am angry that this little illness has slowed me up.’

Time, the novelist’s most precious possession, was fast running out. Fitzgerald, like Stevenson, Dickens and Austen, must have known that he was in an unwinnable race against the clock. His final mention of The Last Tycoon was in a letter to Zelda, where he claimed he was three quarters of the way through. The only person he was fooling was himself. He died on 21 December, not with seventy thousand but just forty-four thousand words in the bag. According to his biographer Matthew J Bruccoli, the last royalty statement for the greatest American writer of his age showed that in 1940 he had earned $13.13, in part thanks to the sale of seven copies of The Great Gatsby.