Wait, didn't she hear him imply that he'd live with her parents?
Which suggest he'd thinking of a long term relationship.
[Oh really.  I've been living apart from my parents for a very long time
but living with your parents isn't bad at all . . . ] . . . usually imply an open question.
"Pay attention Baek Hee" 
[You wish me to live with my parents until I die?] 
Nah
The question is [You wish us to live with my parents until we die?]
Am I making too much of it. 
Thank! 
@thebenefactor