Her family lived outside the city 'proper'. [=lived in an area that was close to the city but was not actually in the city]
Please put your shoes in their 'proper' place. [=please put your shoes where they belong]
The children must learn how to behave 'properly' [='appropriately'] in church.
(..) Oooh! It tingles me. I'm surrounded by idiots. Not you Scar, I mean, you're one of us. I mean, you're our pal. Charmed. Ohh, I like that. He's not king, but he's still so proper. Yeah. Hey, hey hey. Did ya bring us anything to eat, Scar, old buddy, old pal? Huh? Did-ya-did-ya-did-ya? (..)1994 The Lion King