Originally, theatrical props were actually the property of the production company. Not always true today, as films use real or theatrical bills in scenes where money is shown (in a casino, for instance). An interesting question is whether the casino's real money and chips are "movie props) or just like part of the furniture and belong to the set.

Here's an article on the subject:

http://priceonomics.com/the-business-of-fake-hollywood-money/