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Does an intelligent undead, such as a vampire, mummy, etc, have a soul? Is it the original soul of the person they were before?

There was already a question exactly like this specifically for 3.5e but is it the same in 5e?

Does an intelligent undead have a soul?

Why I want to know:

I am wondering if the intelligent undead could use Magic Jar to possess a Humanoid. They'd need to have a soul in order to do that. The spell doesn't say the caster has to be humanoid, only that the possessed creature must be. I'm also wondering if the intelligent undead has a soul, because if not, then the soul escapes upon the death of the person becoming, say, a vampire, and then might inhabit a mature clone they'd prepared in advance of becoming a vampire.

It varies by type of undead.

Each individual monster's description describes whether or not it retains its soul. This can include:

• 
  Souls without bodies: Some undead are souls. The ghost is a soul of a creature, bound to a specific place. The specter and will-o-wisp are corrupted souls.


• 
  Bodies without souls: Zombies are just bodies animated by necromancy or the like. The spell animate dead restores a body to "a foul mimicry of life", and says nothing about restoring the soul which departed at the original creature's death as per DMG p.24.


• 
  Bodies with souls hidden elsewhere: The lich, for example, keeps its soul separate from its body and hidden in a phylactery.


• 
  Bodies with souls intact: The revenant is an example of an undead whose soul inhabits their original body.


• 
  Unknown: In some cases, it's not specified.

By default, a creature's soul departs its body when it dies. Therefore, an undead's body doesn't contain its original soul unless otherwise specified, either by some rule or the DM's decision. DMG p.24 states:

When a creature dies, its soul departs its body, leaves the Material Plane, travels through the Astral Plane, and goes on to abide on the plane where the creature's deity resides. ... Bringing someone back from the dead means retrieving the soul from that plane and returning it to its body.

There are no general rules for whether intelligent undead retain souls. The general rules on undead don't clarify either. MM p.7 merely states:

Undead are once-living creature brought to a horrifying state of undeath through the practice of necromantic magic or some unholy curse.

Magic jar?

Nothing about magic jar says you have to be a living creature to cast the spell or to use it to possess a humanoid. The text does say that once you've cast the spell you can later choose to return to your "living" body, which obviously makes no sense if you weren't already living.

The two possible interpretations are:

• You can't return to a non-living body; "living body" means that you're stuck in the gem if someone murders your comatose body while you're in the jar


• You can return; "living body" just clarifies that your comatose body does not die while you're in the jar.

Since this is ambiguously worded, by the rules it's up to the DM to adjudicate this rare case.

An undead may have a soul, but it probably cannot cast Magic Jar.

Unlike previous editions of D&D, the undead creature type is just a classification in 5th edition. While undead creatures may be affected differently by different spells and supernatural effects, the system doesn't define inherent or automatic consequences of being undead. Instead, the Monster Manual (p7) simply provides this general description:

Undead are once-living creatures brought to a horrifying state of undeath through the practice of necromantic magic or some unholy curse. Undead include walking corpses, such as vampires and zombies, as well as bodiless spirits, such as ghosts and specters.

Because 5th edition doesn't specify whether all undead do or do not have souls, the restriction would vary by the specific creature. In other words, a DM could reasonably make a homebrew undead that has its own soul.

However, the wording of Magic Jar may prevent undead from casting it:

The only action you can take is to project your soul up to 100 feet out of the container, either returning to your living body (and ending the spell) or attempting to possess a humanoids body.

The spell requires the caster to have a "living body". And from the MM description, an undead's body is typically not considered "living". Thus most undead would be unable to successfully use the spell, unless they had a living body.

It appears so.

Searching the Monster Manual, we can see several mentions of souls. While not all are listed below, I didn't find any contradictions among the other undead in the book. (Emphasis mine in all quotes)

From the ghost entry (MM p.147):

A ghost is the soul of a once-living creature, bound to haunt a
specific location, creature, or object that held significance to it in
its life.

From the lich entry (MM p. 203), while the lich itself doesn't have a soul contained within the body, its soul still holds it to the world via the phylactery:

A lich is created by an arcane ritual that traps the wizard's soul
within a phylactery.

Revenant (MM p. 259) states:

Hunger for Revenge. A revenant has only one year to exact revenge.
When its adversary dies, or if the revenant fails to kill its
adversary before its time runs out, it crumbles to dust and its soul
fades into the afterlife.

The least promising mention is of normal skeletons (MM p. 272), which mentions spirits:

An animated skeleton retains no connection to its past, although
resurrecting a skeleton restores it body and soul, banishing the
hateful undead spirit that empowers it.

It however appears the terms spirit and soul can be used interchangeably, as we can see from the Crawling Claw (MM p. 44) there can only be one spirit per creature, which can pass on.

If a dead murderer's spirit already manifests as another undead
creature, if the murderer is raised from death, or if the spirit has
long passed on to another plane, the ritual fails.

So it appears that even non-intelligent undead possess a soul.

As for using the Magic Jar spell, there are a couple problems, as seen below (emphasis mine).

If the container is destroyed or the spell ends, your soul immediately
returns to your body. If your body is more than 100 feet away from you
or if your body is dead when you attempt to return to it, you die

While it seems an undead can cast Magic Jar and transfer their soul into it, it's an irreversible process.