I was thinking the same thing... I am just making myself believe that there is a door leading to a bathroom inside the cage. Maybe, the one shown on the bath tub scene....
Usually pets have those poo areas, and feeding areas. But I'm gonna assume he takes him out for a bath at least. In many of these Stockholm manhwas/mangas I've seen, they still take care of their captives. I mean, JunSeo obviously treasures him.
I wonder how he goes to the bathroom tho(≧∀≦)