This phrase is not taken literally. It means consuming a lot, not actually causing someone to lose their home. Every time my cousin stays over, he eats me out of house and home, but thankfully my pantry is still full!
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Exaggeration
The phrase often exaggerates for humorous effect, implying someone eats a lot but not to an extreme extent. Our new puppy is small, but she could eat us out of house and home if we let her!
Pro Tip 3/3
Informal Use
Used in informal conversations, often within families or close relationships to tease or show mild exasperation. My brother is back from college and is eating us out of house and home!