How does unused money effect the economy?

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This discussion is not just about "unused money", such as money in a savings account for a long period of time. This discussion is about those dollar bills that people will not use because they are really old or torn. I was sitting in my girlfriends room last night and looking at her wall and realized she had a torn 20 dollar bill that she will not spend (I am not even sure if it is...spendable). I am starting to wonder how these unused bills effect the economy. Its not even unused money that a person intends to spend at some point. This 20 dollar bill has been with my girlfriend for like 3 or so years (I think). So, has anyone ever thought about this?