Persona 3 Spoilers will follow this backstory at all times.
A year or so into all of this, the young child, now living in a foster home and trying to block out the world, becomes quite unhappy. One night, he meets the figment of Death locked up inside of him--a young boy who names himself Pharos. The young men become fast friends.
The child's adoptive parents worry that he may have a mental illness, seeing as only he can see the young boy inside of him. Death gains human emotions by playing, interacting, and watching the child... and he learns of how unhappy he is. Conscious of this, and saying that they'll always be friends, he offers the boy a choice: if you're sick of this reality, would you like to escape it?
... The choice is a tempting one. Death and the boy will trade places in spirit and body... by doing so, Death himself can experience freedom, and the boy can shut out the pain of being alone and stop changing; stop growing up.
The boy is given one week to think it over.
After this week, the boy has decided he will go through with this deal. Pharos tells him he can stay a child, and it will likely be permanent. The boy says that he has lost so much, now, and is so tired of moving from foster home to foster home that he would rather it be that way. He was tired of changing.
And the deal is struck.
During the next Dark Hour, Minato Arisato and Pharos switch places... Minato will now be the unseen one. But it's alright, the boy says, because he doesn't like talking to anyone else unnecessarily, anyway. So what if he changes his existence? He liked it better this way.
They both did.
Since it is performed during the Dark Hour, and the boy is still too young to recall it well, his memories of all these events become sealed once they switch places. Even the foster parents and those around him seem to have altered minds, now....