The families handing over the children are at wit’s end. They typically adopted children with serious emotional troubles who, they say, brought fear, chaos and sometimes violence to their homes. Parents of one adopted boy said they felt they had to lock him in his room every night for the safety of everyone else.

“I am totally ashamed to say it, but we do truly hate this boy,” one woman in Nebraska wrote about her 11-year-old adoptive son from Guatemala.

Another mother wrote of re-homing her 12-year-old daughter: “I would have given her away to a serial killer, I was so desperate.”

By some accounts, 10 percent to 25 percent of adoptions don’t work out. That could mean 24,000 foreign-born children are no longer with the families that adopted them, Reuters calculates.

When an adopted child is American, he or she can go into the foster care system. With foreign adoptions, it can be harder. State foster care systems are more reluctant to take custody of children from international adoptions, and giving a child to the authorities may entail an investigation for abuse or paying for the child’s care until new parents are found.

For those who take in re-homed children, it amounts to free adoption, saving many thousands of dollars. A dangerous pitfall is that because there is often no screening to protect the vulnerable children, re-homing can lure pedophiles.

The heart of the Reuters investigation concerns a woman, Nicole Eason, who lost custody of her own two children after one suffered broken bones and who was the last to see a friend’s baby alive before he drowned in a bathtub. Eason acquired six children through re-homing on the Internet.