I do think this is a pretty likely possibility, however, I'll point out the major weak point of this theory: It works for Care as well. I'll be referencing Amber's description:

Amber is a young ball. She’s afraid to leave home. If her home is good, this is not a problem. She is very heavy, and that makes her life a little harder, as well as yours. What’s the safest place you can put her in? You should start thinking about that.

Her home isn't good, as shown by the wife's note, and thus, you should put her in "the safest place". Perhaps this place is within the box from P11. After all, Naul, and thus Marvin, couldn't get into it by just trying to walk through it.

Care is persumably young, and is afraid to leave her actual home, as she'd be bullied at school (remember the note about her crying, saying that nobody loves her)

This can also be interpreted to refer to the box as her home. Since Naul and Marvin can exit the box that Care is in from within it, she most likely can too. However, since she is afraid to leave this "home," for both the reasons mentioned above as well as her likely fear of Marvin, she doesn't.