If you live rent-free, you use a house or a room and you do not pay rent. A rent-free flat uses the same idea as a describing word. A parent may let a grown child live rent-free; a job may come with a rent-free room. Though actually, you may still pay water and electricity, so rent-free does not always mean “costs nothing.” Online, people also joke that a song or a worry is living rent-free in my head — they cannot stop thinking about it. That is a playful stretch of the housing meaning, not a school sense, but you will see it. In housing talk the word is plain and ordinary.