If you cast a "successful" Dispel Magic in the following cases, what are the possible outcomes?

1. An active Conure Elemental spell, i.e. the caster is maintaining concentration at the time you cast Dispel Magic on it.


2. An elemental that is the result of a Conjure Elemental spell where concentration has been lost, i.e. when the following condition described in the spell has occurred:

If your concentration is broken, the elemental doesn't disappear. Instead, you lose control of the elemental, it becomes hostile and might attack. It can't be dismissed by you, and disappears 1 hour after you summoned it. (PHB p.225)

I would like to know in what case, if any, the Elemental disappears as a result of the Dispel Magic.

Case 1) The spell ends and the elemental disappears:

The clause about concentration does not apply, the elemental exists as the effect of an active spell, if the magic is dispelled the elemental goes.

Case 2) There is no spell to dispel, the elemental is unaffected:

The spell has already ended as concentration has been broken and Conjure Elemental is a concentration spell.

Conjure Elemental (PHB p.225)

Duration: Concentration, up to 1 hour

Concentration (PHB p.203):

Some spells require you to maintain concentration in order to keep their magic active. If you lose concentration, such a spell ends.

Therefore while the elemental persists for an hour after the spell ends, it is no longer part of an active spell effect so there is nothing to dispel, the elemental became free of the summoning spell when concentration was lost.

Another way of looking at it is after the spell ends due to loss of concentration, the elemental exists as an environmental change rather than a spell effect. It can't be dispelled any more than the environmental effects of a delayed blast fireball (PHB p.231) can be dispelled following loss of concentration.

In both cases, the elemental disappears

Case 1) The spell ends and the elemental disappears:

The clause about concentration does not apply, the elemental exists as the effect of an active spell, if the magic is dispelled the elemental goes.

Case 2) The spell is still active, it ends, and the elemental disappears:

Normally spells end when the concentration required is broken and Conjure Elemental is a concentration spell, however, Conjure Elemental has a clause that specifically overrides the general rule for concentration spells ending:

If your concentration is broken, the elemental doesn't disappear. Instead, you lose control of the elemental, [...] and it disappears 1 hour after you summoned it.

There is also the line:

The elemental disappears when it drops to 0 hit points or when the spell ends.

Since the elemental doesn't disappear when the concentration is broken, the spell can't have ended, and Dispel Magic is free to end the spell and make the elemental disappear.

See this Sage Advice where Jeremy Crawford implies (strongly, but in classic JC pattern refuses to clearly state) that a casting of Conjure Elemental doesn't end when concentration is broken.

The Elemental vanishes in both cases

In the first case, the elemental is part of an active spell effect, so dispelling it causes the elemental to vanish. This is pretty cut-and-dry.

Less so for the second case.

Is the Disappearance of the Elemental a Spell Effect?

Normally, spells end when Concentration ends. For the vast majority of spells in 5th edition D&D, this is true, and does not need adjudicating, but for the case where the Elemental has broken free, we need to decide whether the spell has ended or not.

The hint that, to me, says the spell continues after concentration is broken is in the mechanism by which the elemental vanishes:

If your concentration is broken, the elemental doesn't disappear. Instead, you lose control of the elemental, it becomes hostile and might attack. It can't be dismissed by you, and disappears 1 hour after you summoned it.

^{Emphasis mine}

The spell's description doesn't specify what kind of mechanism is being used to cause the Elemental to vanish. It only says that, as part of said description for the spell's effect, the Elemental vanishes. Therefore, the effect that causes the Elemental to vanish is part of the spell's effect, and dispellable.

Counterpoint: what if it's not a spell effect?

In order for this effect to not be dispellable, the effect would need to be provably a non-spell magical effect. There's a couple of ways this could be true.

The description for Conjure Elemental could contain a passage like this:

If Conjure Elemental's final effect were a non-spell effect:

"and 1 hour after you summoned it, the plane from which the elemental came from pulls the elemental back, causing it to disappear"

But the spell contains no such language.

Alternatively, the vanishing of the elemental would be a non-spell effect if it were an innate property of the elemental. But there are no Elemental creatures in 5e that have any Plane-shifting ability, or a "time limit" that causes them to return to their plane of origin.

The only other possibility is that the Inner Planes (where most elementals come from) would need to describe such a phenomenon that "pulls" rogue Elementals back to where they came from. But at least in the Player's Handbook, there's no such description.

Conclusion

Because the vanishing of the Elemental is

• Described as part of the effects of a spell, and


• Not explicitly described as being the effect of some other natural phenomena (magical or otherwise),

We therefore conclude that the vanishing of the elemental is a spell effect, and therefore dispellable. And because the spell specifically says the elemental vanishes when the spell ends, the elemental must vanish when the spell is dispelled.