In that case it would go to GoDaddy auction 1 week before the owner loses the right to renew it (which then is a really small chance). The highest bid gets the domain in case owner fails to renew.
http://www.domainsherpa.com/chris-ambler-domain-name-expiration/ they talk about the best drop catching services. I'm guessing you already know that the owner can still renew the name over a month after expiration. Some people will wait till after month then transfer it rather than pay redemption. Anyways good luck with that