On 22 September 1973, Nobel laureate Pablo Neruda – whom Gabriel García Márquez dubbed "the greatest poet of the 20th century" – received some visitors at the Santa María hospital in Chile's capital Santiago. Among them were Sweden's ambassador Harald Edelstam and the Mexican ambassador Gonzalo Martínez Corbala, offering a plane to fly Neruda and his wife Matilde into exile.

We know about their conversation thanks to as yet unpublished documents at the National Archive in Sweden. Edelstam asserts he found the poet "very ill" though still willing to travel to Mexico. In a memo sent to his superiors, Edelstam observes: "In his last hours [Neruda] either didn't know or didn't recognise he suffered a terminal illness. He complained that rheumatism made it impossible to move his arms and legs. When we visited him, Neruda was preparing as best he could to travel … to Mexico. There, he would make a public declaration against the military regime."

That made the poet dangerous to some very powerful people, who had shown they would stop at nothing to defend their interests. They had ousted his friend, Salvador Allende, from the presidency less than a fortnight earlier. Allende died in a coup that was as much about silencing dissident voices as bringing about regime change. Another voice, that of popular singer Víctor Jara, was cut off four days later. Neruda remained. He was perhaps the loudest. His face certainly the most recognisable worldwide. He was too dangerous.

Members of the junta are on record expressing the view on the morning of September 22 that if Neruda flew into exile, his plane would fall into the sea. In the afternoon, radio stations under military control announced the poet would probably die in the next few hours, at a time when he was still awake in the hospital. The following day he was dead.

That historical mystery alone explains why his body was exhumed this week. But there are more pressing reasons too, at a time when the destiny of the left hangs in the balance in Latin America. The death of Venezuela's Hugo Chávez, one of many leftist leaders in the region to have fallen ill to cancer, has combined with the 700 documented assassination attempts against Cuba's Fidel Castro to fuel all manner of conspiracy theories.

More important still is the fact that, faced with an economic crisis without foreseeable end and few alternatives, a new generation of world activists needs to reconnect with the vibrant political imagination embodied by Neruda. The question is not merely whether the commitment he exemplified is possible now, but whether technology, and the institutions we use to manage it, can allow the kind of freedom Neruda called for in his poetry.

In this context, Neruda's life, as well as the shadows cast by his death, are Google-bombs waiting to be set off by a new generation of networked freedom fighters at the heart of our austerity-obsessed, repressive, and frankly boring narratives.

Neruda wasn't surprised by the 1973 coup – most people knew that the consequences of restoring "economic order" would be vicious, and many accepted it as necessary – but it wasn't inevitable: under a deal accepted by the government coalition as well as the opposition, President Allende was going to call for a referendum and would have resigned if the result went against him. This made any show of force by the smaller but influential sector within the Chilean armed forces unnecessary. But the conspirators were bent on regime change, so they brought forward the date of the coup, subjecting Chilean society to a trial by fire in order to cure it of a supposedly menacing communist "cancer".

The invocation of "cancer" to provide yesterday's rulers with a pretext to unleash war abroad and repression at home is mirrored by the questions being asked about Neruda's cancer today.

Neruda and the other individuals behind the Chilean revolution of the early 1970s made mistakes and were at least partially responsible for the consequences. But the real story behind their defeat and deaths hasn't been told yet. This is one of the reasons why people are looking to unearth new truths, hoping to shed some light on the origins of our problems today.

Through histories, testimonies, and documents declassified in the US or revealed as recently as last year by Wikileaks, we now know that the fate of Neruda and others like him had been decided long before they had any hand in mismanaging the economy or dividing political opinion. Persecution of the left had begun in Chile as early as 1948, at the behest of a US government awash with anti-communist paranoia.

That year, a controversial measure known as "the Damned Law" ("la ley maldita") outlawed the Chilean Communist Party, sent the communist leadership into exile and imprisoned hundreds of militants at the Pisagua camp under the orders of a young lieutenant named Augusto Pinochet – the concentration camp's director who would become Chile's dictator, and a friend and inspiration to Margaret Thatcher.

Neruda, radicalised like many others by the anti-fascist struggle of the 1930s and 40s, chose to flee the country. Fearing for his life he crossed the Andes on a horse, carrying with him the manuscript of his epic poem Canto General, before resurfacing in Mexico thanks to the help of his friends Pablo Picasso and Diego Rivera.

His second exile would have been in 1973. Edelstam's conversation with Neruda took place a mere two hours before the poet went to sleep, never to wake up again. When the Swedish diplomat went to Neruda's house to offer his condolences, he found it destroyed. Pinochet's men were bent on erasing every trace of his existence. They would do the same with thousands of people during a reign of terror that would last for nearly two decades. That is why so many people this week are holding their breath to find out what clues Neruda's exhumed body might hold.

• Oscar Guardiola-Rivera's Story of a Death Foretold: The Coup against Salvador Allende, 11 September 1973 will be published by Bloomsbury in September