Is it believable that the sole survivor of a terrorist attack, a sixteen-year-old amnesiac boy, be taken in as a foster child with the sheriff to live with the sheriff's family until his (the boy's) identity is discovered? That, because his identity isn't discovered, he slowly becomes part of the sheriff's family?
Except for emergency, short-term placements with relatives or close family friends, foster care providers have to be licensed before any children can be placed with them.
Could the Sheriff and his wife become licensed, then his wife die of cancer, and he forget that he was still licensed? When this boy is discovered, the Sheriff's compassion as well as ability to shield the boy from the media convinced him to go ahead and serve as a foster parent for the boy?
Licenses only last a certain period of time--often it's 2 years--so it would have to happen within that time frame. I should note that the sheriff does not have any say over where the child is placed, as that is left up to the local child welfare agency. However, members of police departments generally have working relationships with child welfare officials, so maybe he knows a higher-up in the agency and can convince them he would make a great foster parent.
It sounds like you just need to work out the technical details, especially given @Ben414's advice. This sounds fine to me as long as you do work out those details.
