Unless you have a feat that gives a +1 to saving throws (like human preseverence), you never add anything to a saving throw, death save or not.This is where my question. The book says that they have 3 chances on saving throws. In PH1, it states: lower than 10, you slip one step closer; 10-19, no change; 20 or higher, spend a healing surge (basically live and be knocked out). It doesn't say what state you are supposed to add with the roll.