With no letter approving her birth, Li’s parents were faced with the prospect of paying a hefty fine (for breaking the one-child policy) to register her but could not afford to do so.

Since then it has been a two-decade battle with officials until China scrapped its one-child policy last year and Li finally received an official paper to prove her existence.

Ending the one-child policy has left people like Li scrambling to make up for lost years, resentful as they fear this recognition may have come too late and unsure what the government is going to do to help them make up for those years.

Li missed out on an education and struggled to learn everything by herself, using library books borrowed under her elder sister’s name, with her family unable to afford a tutor.

“My mother was dismissed from her job because she gave birth to me,” Li says in an interview at her home in Beijing, a shabby house without a private toilet and with a makeshift shower. “All four of us had to live off my father’s meagre salary.”

Li’s mother, Bai Xiuling, a former factory worker, says her daughter used to cry when other children set off for school. “She wanted to study at school, but she can’t. My child has already missed the nine-year compulsory education. No money can buy her time back,” she says.

According to China’s latest population census, conducted in 2010, there were 13 million unregistered citizens like Li, almost one per cent of the country’s total population.

“Most of them are children born outside the country’s one-child policy,” says Ma Jiantang, the then head of China’s National Bureau of Statistics which conducted the census.

A 2015 study by the Academy of Macroeconomic Research at the National Development and Reform Commission found nearly half of China’s unregistered citizens were illiterate or lacked formal education.

During the years of the one-child policy, second children would not be registered in the household system unless a hefty fine was paid, although there were some exceptions to this rule.

Births out of marriage are also considered a violation of China’s strict family planning rules, and unmarried couples had to pay a fine to register their newborn.

China is one of few countries which has a household registration system, known as hukou, that contains information on citizens such as births and marriages. A person without a hukou is denied public services, such as education and health care, and is barred from getting married, finding a job or even opening a bank account.

The link between the one-child policy and hukou is controversial, with policymakers saying the household registration system is open to all citizens without any conditions. But families affected say the link was clear.

“Although China’s household registration and one-child policy shouldn’t have been bound together, local authorities have been doing so for years because they found it useful to force families to comply with the family planning law,” says Wu Youshui, director at Zhejiang Bi Jian Law Firm.

Wu, who assisted many Chinese couples to register their second child, adds there is also an economic incentive, as people who had children born without permission were unable to register them unless they paid a hefty fee which became a lucrative source of local revenue.

Data that Wu obtained from 24 provincial-level governments under the country’s open government information regulations found that in 2012 alone, the authorities collected more than 20 billion yuan (HK$22.34 billion) in fines from parents.

“None of the governments were able to fully account for how the money was spent,” Wu says.

Yang Wenzhuang, an official at the National Health and Family Planning Commission, denies the one child policy – and punishments associated with it – have played a role in blocking millions of citizens from being registered.

At a press conference earlier this year, Yang said his department had tried its best to remove hurdles set by local authorities in household registration and many unregistered citizens have now been included in the hukou system.

Unmarried mother Liu Chunyan, a freelance English teacher, says she was unable to pay the fine so she kept her daughter’s birth secret for seven years until last April when she finally registered her child.

“The fine in Beijing was really high. I thought about it over and over again, but still I dared not to let the government know that I have a child born without permission,” she says.

Due to a lack of hukou, Liu’s daughter had no access to government-subsidised health care. She was unable to buy train tickets or travel abroad.

“When other parents took their kids to Hong Kong Disneyland, we couldn’t even think of it,” Liu says. “My daughter is now seven years old, and she has never set foot outside Beijing,” she says, adding that she is still worried that government officials might ask her to pay the fine.

Despite all the concerns, however, Liu calls herself “lucky”. Last year, she tried but failed to find a place for her daughter to study, due to a lack of hukou. “Now, my daughter has everything she needs to go to public school,” Liu says.

But others are not so lucky, with researchers from the Academy of Macroeconomic Research saying more than half of China’s unregistered citizens are above 18 years old. Many of these adults not only lost out on schooling, but also struggled to find a job as they couldn’t provide hukou and other legal documents often needed for hiring.

For example Liu Wei, from Henan province, had no choice but to work in a coal mine.

After the mine was closed, Liu couldn’t find another job and ended up sleeping on the streets for five years, its report says.

The social isolation can also pass from one generation to the next, and the researchers are unsure how the end of the one-child policy would impact those people.

“Quite a lot of unregistered children in China have grown up and started their own families, creating the second generation of unregistered children,” the report says.

Huang Wenzheng, a demographer and a former assistant professor at the Harvard T.H. Chan School of Public Health, says the government tried to address this problem after the 2010 census.

“As far as I know, many unregistered children now have their hukou … the Chinese central government has begun taking household registration seriously,” Huang says.

“The government has recognised having so many citizens unregistered is a serious problem. It not only takes a toll on social development, but has caused huge pain to many families.”