I've never used GoDaddy's "negotiation" services, but I have used them to "backorder" a domain. If the current owner lets anything lapse, you have a chance of getting the domain. It rarely works out, but I have gotten a few good domains that way. I think they charge around $18 to backorder a domain. There are, of course, other registrars that provide the same service...or you can just build your own script to monitor for changes.
