You can stay on-board if you want to. I have met many people that do exactly that.
Ships services such as food and bar service still go on. The casino and the ship's stores are closed.
It's less crowded by the pool and quite relaxing because most people do get off the ship.
Enjoy your cruise.
Carnival Liberty New Year's Eve 2007
Liberty of the Seas 5/2008+11/2009
Allure 1/16/ 2011
Independence of the Seas 12/29/2013 Top-notch!