In addition, going through the black market is often less onerous than paying penalties for a second child under China's one-child policy.
To break their resistance and keep them quiet on long journeys, some of the older abducted children are abused or told that their parents divorced and abandoned them. In some cases, children pass through seven or more middlemen.
The markup can be substantial. Those who snatch the kids can expect to get $36 to $60, according to confessions of those caught, still a substantial sum in a country where the average income is about $100 a month. Middlemen can sell them for $400 or more, with the end buyer paying upward of $1,200 for "substandard goods," or girls, and $2,000 for "quality goods," or boys.
As if losing a child isn't enough, desperate parents are often besieged by con artists once they appeal to the public for help in finding their children. These ploys range from petty scams -- Cheng lost $5, about a day's wages, to someone who said he had seen his daughter and could provide a picture of her and the kidnapper -- to life-or-death threats and demands for huge ransoms.
Parents say they can't find words to describe the people who would stoop so low as to steal someone's children. "For a nation, the loss of a child may be small," said Wang Chunkai, 33, a firewood seller whose daughter was taken in front of his brother's house. "But for a family, it's as big as the heavens."
Wang says that if he ever found the kidnapper, he would like to stab him, not once but repeatedly. Jiang Xinzhou, a 34-year-old engineer whose 2-year-old daughter was snatched from her house while her parents were home, says he would separate the criminals from their own children so they could experience a fraction of the pain.
Most parents voice strong support for the government's use of the death penalty against child thieves.
The government has carried out several executions in recent years, and handed down a death sentence last year to the head of a ring that sent dozens of children to Singapore over a five-year period.
But parents of the missing say the state should also come down heavily on those who buy children. Buyers are subject to a three-year jail sentence, but the law is almost never enforced.
As Cheng and Jin look over their two-room apartment, they are overcome with grief. They show snapshots of their daughter, touching her face in the picture in a bid to make a connection. Her image comes back to them through the day as they wonder what she's doing, how she misses them, whether she's crying or hungry or sick.
"Our loss is so great, I feel numb and thought about killing myself," Cheng said. "But I realized this wouldn't be fair to the rest of my family. We failed her as parents, but I won't give up hope she'll come back. I'll never give up hope."
Yin Lijin in The Times' Beijing Bureau contributed to this report.
