The disappeared: At least 26,000 people have gone missing in Mexico's drugs war

One by one they gather in front of Saltillo's imposing cathedral in the city's historic Plaza de Armas square, wearing white T-shirts emblazoned with names, photographs, dates. Tentatively they begin to chant, "Where have they gone, where have they gone, where have our sons and daughters gone?"

These mothers, fathers, grandparents, children, brothers and sisters have gathered in protest, as they try to find out what has become of their loved ones – the missing victims of Mexico's brutal drug wars and rampant corruption – trying, because nobody else is willing to help them.

Saltillo is the capital of Coahuila, a state in northern Mexico that borders Texas, which, four years ago, became a deadly battleground for cartels fighting over territory. The border regions are crucial transportation routes for drugs – heroin, marijuana, cocaine and methamphetamine (better known as crystal meth to Breaking Bad fans) – destined for the insatiable American market.

Violence erupted on the streets when the old power bases were disrupted by internal splits, a proliferation of new cartels and President Felipe Calderon's ill-fated "drug war" between 2006 and 2012. This war left at least 60,000 dead across Mexico, and swathes of the country awash with bullets and blood. The major battle-grounds have shifted further south of late, but another 14,000 have died since Enrique Peña Nieto came to power last December, according to analysis by respected news magazine Zeta.

Worse, public authorities have become so corrupt that clear boundaries between the cartels and state, between the dirty and clean, no longer exist. Politicians, prosecutors, police and armed forces in Coahuila, its northern neighbours Nuevo Leon and Tamaulipas and a depressingly large number of other states are involved in the production and transport of drugs, weapons and people.

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In February, a new figure shocked even those desensitised to the daily horrors: 26,000 people were reported missing or disappeared during Calderon's six-year rule, and the authorities have no idea what became of them. Interior Ministry figures revealed that in 40 per cent of cases, a criminal investigation was never even opened.

The 100 or so families who gathered in the Plaza de Armas on International Day of the Disappeared at the end of August did so in spite of the intimidating presence of heavily armed state police officers scattered around the square. It was a bold display of courage and defiance by ordinary people who are as despairing as they are hopeful. As they walked together hand in hand, their voices grew louder and more confident with each verse, drawing strength from one another.

For years, families suffered alone, often too afraid even to talk about the crime never mind report it to the authorities. Those who dared demand an investigation were frequently met with ineptitude, corruption and disinterest. They were told to give up their son or daughter for dead, or accept that they had suddenly left to join the cartels. The riposte came in 2009, when four families searching for missing relatives founded Fuerza Unidas por Nuestros Desaparecidos en Coahuila (Fuundec – United Forces for Our Missing in Coahuila), believing that together they would be harder to ignore or intimidate.

Jorge Verastequi Gonzales, a mature, compassionate 22-year-old, co-founded the group after his older brother and nephew were snatched by armed men on their way home from a religious service in Parras de la Fuente – a beautiful oasis brimming with vineyards in the middle of the Coahuila desert. "We are a movement of families trying to find our missing loved ones," says Gonzales. "We are victims trying to fill in the gaps left by the state. We carry out our own investigations then pressure the authorities to pursue the lines of inquiry. Our public demonstrations build pressure on the authorities and make this humanitarian emergency, this tragedy of the disappeared, visible to the world."

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In reality, this means the families themselves tracing phone records, interviewing witnesses, tracking mobile-phone signals, scouring land-registry records and even commissioning their own forensic tests. Fuundec gets these families in front of state and federal officials, and doesn't allow the officials to close files, dismiss leads or bully the families into giving up. The movement has so far spread to eight more states.

Their diligence in Coahuila has provided an invaluable insight into Mexico's disappeared. Fuundec knows of 321 people who have disappeared in the state since 2007 in 143 separate "kidnappings" (the true number is almost certainly closer to 500). This includes the disappearance of 23 male bus-company workers attending a meeting on a ranch in April 2009 (only two families reported a disappearance). Of that 321, just seven have been found so far: two rescued during a police operation (by chance rather than design), three freed by their captors, one (who was mentally ill) found with the help of a journalist, and the seventh found dead – killed by his captors. More than half the victims are under 35; 17 per cent are women. They include housewives, engineers, students, bus drivers, street vendors and business owners. Money rarely seems the motive, as genuine ransom demands are rare.

Fuundec says it has strong evidence in more than 10 per cent of its cases that state agents – local or federal police, army or navy officers – directly participated in the disappearances.Human Rights Watch and Amnesty International both found compelling evidence of state involvement in more than half the disappearances they documented across Mexico – but the government continues to focus blame on the gangs.

Yet the grim reports on murders and mass graves have failed to destroy the hope most families still have of finding their loved ones alive. Their faith is in part fuelled by rumours of cartels taking communication technicians, engineers, architects, dentists, builders and all their equipment, to service their vast operations.

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Rupert Knox, Amnesty International's Mexico researcher, is not so optimistic. "There is a natural desire within families to find their loved ones alive, and the systematic failure to investigate disappearances has left them without any solid information. But the fact is, mass killings and disposal of bodies have become a hideous feature of this war in the past few years."

In 2012, according to the National Human Rights Commission, there were 15,921 unidentified bodies around the country. It is not known how many of these remains belong to the disappeared, due to lack of forensic investigations.

Thousands of unclaimed bodies and thousands of families looking for answers – a reprehensible state of affairs which the government, if it had the political will, could tackle.

The relatives of the disappeared interviewed here feel tormented by not knowing what has become of their loved ones. Though let down by those in power, they refuse to surrender. "If I give up hoping, then all I have is my imagination and that's too awful to bear," says one mother.

Back in Saltillo's grand cathedral, Father Pedro Pantoja, a human-rights champion fighting alongside the families, urges patience and resolve. In unison, the weeping mothers and fathers respond: "They took them alive, we want them back alive."

Brenda Domaris Gonzalez Solis, 25, professional cook and mother of two-year-old Antonio, last seen on 31 July 2011

Brenda and her friend were taken on their way home from a night out in what seems to have been a staged car crash in Santa Catarina, a lawless town in Nuevo Leon plagued by police corruption. Her mother, Juana Solis, 49, was in bed when Brenda rang her younger brother asking for help. "She said they'd been in an accident, the traffic police were there, but that he should come quickly. He heard a man telling Brenda to get off the phone, then it went dead."

Her brother rushed to the scene, where the car lay in a ravine, punctured by five bullet holes – but there was no blood. Two traffic police said Brenda and her friend had been taken to hospital by ambulance. The family searched all the hospitals, but no one had seen or heard of them. "We then asked all the local shops for their CCTV but they said it didn't work. One security guard told us he had heard shots fired, but that's literally all we know."

Juana started making noise at the state prosecutor's office, constantly demanding they search for her daughter. One year later they claimed to have found Brenda's remains in a mass grave; Juana was shown a plastic bag of bones as proof. "It was so suspicious – they had never even taken our DNA and they kept pressuring me to let them burn the remains. They wanted me to go away, but I'd lost a daughter not a dog, so we got our own DNA analysis – and it wasn't her."

Juana still has no idea why her daughter was taken, or whether it was a targeted or opportunistic attack, but with no ransom request or body, she remains convinced that Brenda is alive. "My daughter is beautiful, she is a great cook, is good with accounts, so I am sure they've kept her to work. I am her mother; I'd know in my heart if she was dead."

Estaban Acosta Rodriguez, 34, his two brothers and his eight-year-old son Brandon Estaban were last seen driving from Saltillo to Monterrey airport when they were intercepted by three car-loads of armed men on 29 August 2009

Rodriguez was head of security at a local prison, but had recently spent a year at a high-security prison where drug traffickers and other organised-crime bosses were held. The cartels have a reputation for exacting revenge on prison officers who refuse to be corrupted. An anti-kidnap squad investigation focused on Rodriguez's work, but despite three eye witnesses reporting the kidnap, no suspect or motive was identified.

"I don't think my husband had been threatened – he would have told me, I am sure," says Fuundec co-founder Lourdes Herrera del Llano, the childhood sweetheart who Rodriguez married. "It was just an ordinary day and we were just an ordinary family. It's been four years and people say I should try to live my life, but I want my old life back, my daughter wants her brother and father back.

"I promised to find my son no matter how long it takes," adds Del Llano "and I won't give up on him; the pain in my heart is so strong."

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Roy Rivera Hidalgo, 18, a philosophy and languages undergraduate, was last seen on 11 January 2011

It was the last night of the Christmas holidays and schoolteacher Irma Rivera Hidalgo (above) and her boys, Roy, 18, and Ricky, 16, were up late, preparing for the new term. They lived in a residential suburb of Monterrey, capital of the border state Nuevo Leon and Mexico's wealthy industrial hub.

The family chit-chat was halted at 1am as 10 heavily armed men wearing masks, camouflage trousers and flak-jackets with the word POLICE burst in. They ransacked the house, taking computers, phones, jewellery and car keys, and hitting the boys with guns, before the boss demanded to know who the eldest was. "They'd covered my head so I didn't see them take Roy, but he was gone," says Irma. "All I saw was a big muddy car without licence plates speeding away."

By 2011, the local police were widely known to be corrupt, and Monterrey was plastered with official billboards advising people to instead call the army to report major crimes. But within hours of the invasion of the Hidalgo home, an anonymous caller rang the house threatening to kill Roy – so Irma, frantic and unsure who to trust, agreed to pay a million pesos (£50,000) in ransom.

"I said that I'd pay only after I heard Roy's voice. They put him on; he said, 'Mum, it's me, Roy, I love you very much.' I told him I loved him too. That's the last I heard his voice." The kidnappers, who claimed to be with the Gulf Cartel, stopped calling.

"I tried to trace their mobiles, but the phone companies wouldn't give me names. We plotted the movements of my phone, which was stolen that night, using GPS and Google Earth; I took 80 pictures of 16 places where the phone was and gave all this information to the army. The state had all the technology, but they weren't interested; it was left to us."

Two months later, the army conducted a rescue operation on a house where 15 missing people were believed to be held. They recovered two men and a woman who had been tortured, but no Roy. Three men were arrested, but the fate of the other 12 disappeared is still a mystery.

A new army unit then took over Monterrey and showed little interest in Roy's case. It was down to Irma to keep the case open. In 2012, she founded Fundenl – the Nuevo Leon arm of Fuundec – and every week the families of the disappeared hold a vigil in front of City Hall. "The army said Roy was taken as a 'forced recruit' by serving police officers working with a cartel. Whatever the truth is, I have to find out; I won't let the authorities forget him. Some days I think he can't be alive, but they have rescued people forced to work for the cartels [before], so as long as there is no body, we have hope and I keep looking."