Often, people find out about price drops by simply searching the internet travel sites like Travelocity to see how their particular cruise is selling. If they see the price for the cabin category they booked has been reduced they call their agent to see if the cruise line will adjust their price. I have found that the cruise lines will play ball with me provided I haven't paid my balance yet. Once the balance is paid things can get much more difficult. And some lines are less apt to budge on the price. It can get to be quite a game. Sometimes one may have to cancel their booking and rebook to get the new price. Sometimes the cruise line will have some fine print that says someone can't cancel a previous booking and rebook just to get the new price.
Other times, a good agent will be periodically checking on prices and if a clients cruise shows prices going down that agent will take care of it and surprise the client. My agent uses this method, which is why I have stuck with her for over 10 years.
And finally, there are occasions when the cruise line itself will step up and issue a credit to previously booked passengers if the price for their cruise has declined.