D&D 5E - Stake to the Heart, Misty Escape, and Vampires / Vampire Spawn

a) Is a vampire spawn destroyed when simply reduced to 0 hp (regardless of whether it's in sunlight or running water)? If not, why bother with the Stake to the Heart entry (it seems unlikely that it would ever be "incapacitated in its resting place", as it cannot Misty Escape)?

What happens when a vampire spawn reaches 0 hp? The same thing that happens to everything else - it drops unconscious. The DM can choose to have it die on that instant, and usually will, but they need not - if a vampire spawn stabilizes, it will regain 1 hp in 1d4 hours like anything else, and then it'll start regenerating.

The most common scenario where a vampire spawn is incapacitated in its resting place is when it's knocked out and you want to be sure it won't come back, so you stake it, too. Mostly, it's a fluffy thing, but a DM who wanted to make a spawn a recurring threat is well within their rights to require that to For Reals Kill It.

Other effects might incapacitate a vampire spawn that's not at 0 hp, too. For instance, eyebite can knock a creature unconscious and doesn't have that pesky "no undead" limitation that sleep does. Eyebite + a stake is a one-two punch for vampires and spawn in their lairs. Hypnotic Pattern could do it, too.

b) What happens if the vampire spawn (or true vampire, for that matter) is staked when otherwise incapacitated but not in its resting place?

The same thing that happens to anything else - it can't take actions or reactions as long as it's incapacitated, and it takes damage from the stake (assuming the stake hits them - Incapacitated doesn't = Auto-Hit, though at 0 hp you've got advantage). "Incapacitated" is a technical term in 5e, a condition that can be inflicted on creatures through a variety of means. One of those means is dropping to 0 hp, but it's not the only way.

Further confusing things, the Shapechanger ability implies that magical damage would affect the vampire in mist form, by specifically mentioning immunity to nonmagical damage except sunlight. However, while engaged in Misty Escape, it's already at 0 hp. Is this meant to imply that the alternative way to permanently destroy a vampire while it is engaged in a Misty Escape is by dealing massive damage (i.e. > max hp) to it from magic or have it enter sunlight / running water (which would preempt the Misty Escape ability)?

You can damage things at 0 hp - you fail a death save or two, and die if the damage exceeds your maximum HP. So all of those techniques work. Legendary resistance on vampires might make some of those tough, and in Curse of Strahd there's not much running water or sunlight to worry about (though a clever party might have some!). Also, escape is pretty easy - seeping through cracks in the stonework as a gas cloud lets him essentially travel through (non air-tight) walls in his drafty old castle. If he's brought to 0 hp by the wielder of the Sunsword, that's only one failed death save at the start of the turn that he uses to move 20 feet through the walls and get the heck outta dodge (or not even that if he Legendary Action's through the walls).

A vampire in a sealed chamber will have a harder time of it, but even then, three rounds to keep a cloud of gas from escaping is...enough time for something to go wrong.

Just hoping for some clarity on the conditions under which vampires and vampire spawns can be permanently destroyed.

Remember that Incapacitated has a technical definition in 5e. Being at 0 hp applies that, and so does other things.

Also remember that a monster at 0 hp doesn't have to die immediately. Your Vampire Spawn might technically require you to stake them after you've dropped 'em to make sure they're dead (relying on three failed death saves might not produce much success!). Strahd - and any true Vampire - probably should stick around at 0 hp until those three death saves are failed.

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