The results for monsters and creatures when damaged to 0 or below are not analogous. This is on the Player's Handbook p295 (Rules Compendium p260-1)
When damage is dealt, if the result is between 0 or less (up to their bloodied value as a negative number then the damaged character is Dying (and usually Unconscious).
If the damage takes a creature from above 0 to past -(bloodied) then the target is dead, regardless of any desires of the creatures involved.
It is noted that most monsters will not attack characters who are dying. The DM is free to ignore that advice if desired.
There is no general way to make a character unconscious via damage and not dying by the rules although there may be specific abilities or items that allow this.
Monsters, when reduced to 0 or below are dead, unless the characters wish to knock them unconscious. There is no way to get a monster to the Dying condition via damage.
Unconscious is not Dying, the two conditions are similar, but it is only Dying that requires the Death Saving Throw and the resultant minor chance of spontaneous healing.
If you want to prevent Characters from reviving themselves, you need to hit them until they are dead. There isn't a normal option to make them Unconscious instead of Dying via damage.