In the meantime, troubling reports about the family have emerged.

Washington State Child Protective Services learned on Friday of allegations of abuse against the Harts and tried to make contact with them that day, but no one answered when its employees visited their home, Norah West, a spokeswoman for the state’s Department of Social and Health Services, said on Wednesday.

Ms. West said that Child Protective Services had opened the inquiry because of “allegations of abuse or neglect in the home.”

She said the children’s agency made two subsequent attempts to establish contact with the family, visiting the home again on Monday and Tuesday, but was unsuccessful. A spokesman for the Clark County Sheriff’s Department in Washington State said he was not aware of any previous interactions with the family.

A neighbor of the Harts in Woodland, Wash., Dana DeKalb, told the NBC affiliate KGW that Devonte, the child from the 2014 photograph, had recently begun venturing over to her home to ask for food, sometimes several times a day.

According to Ms. DeKalb, Devonte said his mothers sometimes withheld food from the children as punishment and disallowed them from going outside.

Ms. DeKalb said she was the one who brought the family to the attention of Child Protective Services. She told KGW that when the children’s agency visited on Friday, the Harts refused to answer the door, and that the family left only hours later. Ms. DeKalb did not immediately respond to a telephone message on Wednesday night.

Publicly available records show that Sarah Hart had lived in Minnesota for years before eventually moving to West Linn, Ore., and finally Woodland, Wash. Court records show that she was convicted of misdemeanor domestic assault in Minnesota in 2011. A copy of the complaint obtained by The New York Times shows Sarah Hart had also initially been charged with one count of “malicious punishment of child.”