Mainly what was asked above. I know that a melee attack can stun an opponent by reducing them to 0 HP instead of killing them, but can a monster somehow lay down in such a way that the blow is fatal?
No, the creature being reduced to 0 hit points has no say in the matter.
The rules for knocking creatures unconscious state:
Sometimes an attacker wants to incapacitate a foe, rather than deal a killing blow. When an attacker reduces a creature to 0 hit points with a melee attack, the attacker can knock the creature out. The attacker can make this choice the instant the damage is dealt. The creature falls unconscious and is stable.
These are the only rules on the situation, and only the attacker is given a choice.
One way to achieve this is to use Contingency spell:
Choose a spell of 5th level or lower that you can cast, that has a casting time of 1 action, and that can target you.
Choose Magic Missile, which can target any creature you can see see, including yourself. You must use a 2nd level spell slot so you get 4 darts.
it takes effect when a certain circumstance occurs.
As the circumstance, choose "when I drop to 0 hit points".
So when you drop to 0 hit points, you will be hit 4 times. First one will be the "killing blow" in case you were merely knocked unconscious. Following 3 will cause 3 death saving throw failures. Congratulations, you're now dead.
If you are in an unfortunate situation of having a table where Magic Missile causes just 1 death saving throw failure for a single target (as suggested in comments and discussed here), then there is at least one option which may help more than just hitting yourself with any damage spell:
Dimension Door can target yourself, and teleport you 500 feet up in the air. You will then promptly fall down for the maximum fall damage, 20d6, average 70. If that is enough to insta-kill you, great. If not, at least you're now making death saving throws instead of just being unconscious (or, if you were making them already, you get at least one failure). And with some luck you may drop on your would-be captor, as a bonus.
The obvious drawback is, that you need to be a Wizard or a Bard or a custom NPC to be able to cast Contingency, which is a 6th level spell.
You can still be just Revivified even if you just kill yourself. Unfortunately 5th level or below spells do not allow disintegration. Teleportation circle could be a solution, but it can't target "you" so it won't work. If you are in your base, you could use Dimension Door to drop yourself to a pool of acid or something, but if that is an option, you might choose to use it to escape instead of dying, which is out of the scope of the question.