A character who was dying but who has stopped losing hit points each round and still has negative hit points is stable. The character is no longer dying, but is still unconscious. If the character has become stable because of aid from another character (such as a Heal check or magical healing), then the character no longer loses hit points. The character can make a DC 10 Constitution check each hour to become conscious and disabled (even though his hit points are still negative). The character takes a penalty on this roll equal to his negative hit point total.
If a character has become stable on his own and hasn't had help, he is still at risk of losing hit points. Each hour he can make a Constitution check to become stable (as a character that has received aid), but each failed check causes him to lose 1 hit point.
Marius, Scholai Armsmaster Says: A stable creature can still suffer a coup de grace. When facing bloodthirsty enemies, don’t completely ignore your fallen allies.