The sentence should be: While he lives off of/on his benefit, she lives on/off of her inheritance. You could remove the 'of' or leave it in.

If you live on or off something, you derive your income from it and are usually dependent on it. It is a curious twist of language that 'on' and 'off' are opposites, but end up being used to mean the same thing. You could have just as well said "She lives on her inheritance."