The small children of the FAYZ, known as the "Littles", are the ones too young to care for themselves. Under fives lived in the daycare with Mary Terrafino before she poofed. Her brother, John Terrafino, then took over. When a child became older than that, they went off to live with an older kid- a brother or sister or a friend.
When the FAYZ first occourred in Gone, there were numerous baby and small toddlers left alone. Unfortunately, no one realized this until it was too late and lots of tiny children died. (No-one knows how many.) Sam and Quinn did find one baby in a house but it was long dead. They found it because of the stink. No-one really knew what to do.
In the daycare, the Terrafinos find it hard because no-one wants to help and look after the Littles. They begin running out of baby food, kids medicines and nappies.