I rejected an adoption once just to see what would happen.

I didn't know you could sell your children. Are you talking about when the talent scout shows up at the door?

They are probably talking about the talent scout.

I sent a kid away to a talent scout once. He had showed up on my family's doorstep, and two (in-game) years later, I sent him with the talent scout. That was because the parents were old and about to die, and I didn't want him to have to live by himself.
When the parents died, I chose him for the next generation. They had triplets, and one of the triplets found a little girl outside the door. They had two more kids, and when he and his wife died, I chose the adopted girl for the next generation. And that is the story of Nap the orphan.