Every new foster home came with a fresh set of rules. It did not matter how many or how few. It did not matter if they were lax or unreasonable. They would not be obeyed.

In the nine years that Shaquille Samuel spent in foster care, he landed in 16 homes. Impermanence was met with impertinence.

“I had a rough time,” Mr. Samuel, 23, said, adding that he would not listen to anyone. “I was hurting.”

Mr. Samuel, who never knew his father, entered New York City’s foster care system when he was 12, after he and his sister, a toddler at the time, were taken from their mother’s custody. His relocations in the system became more frequent as he grew older. According to Children’s Aid, one of eight organizations supported by The New York Times Neediest Cases Fund, less than one third of the foster families it supports accept children 13 or older.