Well, I just found a reference for Monster Death & Dying Rules from an interesting source - The 2005 version of Dungeons & Dragons for Dummies. Go figure!
On page 78 under the Death and Dying section it clearly states, and I quote "When a monster's hit points are reduced to 0 it is dead and defeated"
IMHO the character is naturally the Hero of the story. The monster is there to slay. Now agreed, for dramatic effect the arch enemy NPC may survive or "linger" on after a grievous wound but it should not be the norm. My thought is that it should be the DM's discretion or part of the story line where this may happen. I just don’t feel like having to roll a D% for every lowly goblin the players may have defeated to see if they stabilize or not.
And, of course, surely Dungeons & Dragons for Dummies could not be wrong......