Are there any fae other than the dullahan associated with death?
There are several actually! See, you could argue that the fae are all associated with 'death' or Other-worldliness at least, since they live in/on a plane different to that of mortals. But specific fae who are associated with death are also present.
Condolences, this is long.
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The Dullahan
As you noted, nonnie, the Dullahan is associated with death. The headless horsemen of Irish folklore, the Dullahan is depicted as a headless rider astride a black horse (of course) who carries his head in a hand which he holds up to see long distances. The Dullahan is possibly the embodiment of the Celtic god Crom Dubh (based on the earlier pre-christianity god Crom Cruach (most likely a fertility god to whom human sacrifices were made prior to the end of his cult worship by St Patrick in the 5th century).
Interestingly enough, a bit of further research into the Dullahan shows that there's an evolution to the whole "Headless Horseman" thing. Prior to Thomas Crofton Croker's three volumes of Irish fairytales from around 1825, the only version of a Dullahan was actually not connected with horses or headlessness at all. Charles Vallancey compares Irish and Arabic folklore to give a definition of the Dullahan as follows:
The Dullahan or Wullahan is a terrible bug-bear at this day; the peasants hear him in the night dragging a heavy chain through the villages and along the roads; this is the wulahan, or Satanas of the Arabs…
So, for Vallancey, the Dullahan is a being that has chains, drags them aong the road, and basically just makes noise on the roads for whatever reason. Croker's Dullahan come in a variety of forms; headless people dancing around, a headless horseman, and a headless coachman. In general, the consensus is less about riding horses and more about being headless and travelling from one place to another.
[I'm showing mercy and putting the rest of this long answer under the read-more]
For the character of Larry Dodd discovers a woman he gave a ride to had no head:
Larry Dodd sprung forward with open arms, and clasped on them—a woman, it is true—but a woman without any lips to kiss, by reason of her having no head! […] staggering like a drunken man, he rolled against the broken window of the ruin, horrified at the conviction that he had actually held a Dullahan in his embrace!
This headless woman led him to other headless persons, other Dullahan, dancing around a fire:
It was strange music to dance by; nevertheless, moving to it, round and round the wheel set with skulls, were well dressed ladies and gentlemen, and soldiers and sailors, and priests and publicans, and jockeys and jennys, but all without their heads.
Who even offered him hospitality because that's just what you do, even if you're headless I guess.
Other iterations of the Dullahan are primarily focused on travelling individuals who happen to have no heads but are not evil in any definitive way. The headless rider involved in the story of character Charlie Culnane is where we get the basic description of the Dullahan seen on Wikipedia:
Charley did look again, and now in the proper place, for he clearly saw, under the aforesaid right arm, that head from which the voice had proceeded, and such a head no mortal ever saw before.
It looked like a large cream cheese hung round with black puddings; no speck of colour enlivened the ashy paleness of the depressed features; the skin lay stretched over the unearthly surface, almost like the parchment head of a drum. Two fiery eyes of prodigious circumference, with a strange and irregular motion, flashed like meteors upon Charley, and a mouth that reached from either extremity of two ears, which peeped forth from under a profusion of matted locks of ustreless blackness.
Culnane earns favour from the Dullahan by challenging him to a race. Any bets he makes about horse-races essentially will always pay off because he raced the Dullahan.
The headless coachman is where we get the Dullahan being a death-omen:
The appearance of "The Headless Coach," as it is called, is a very general superstitions, and is generally regarded as a sign of death, or an omen of some misfortune.
The more modern understanding of the Dullahan then is based on Croker's versions in his fairytale collection and combined into a singular being that shares a lot of basic similarities to the Headless Horseman of, like, Sleepy Hollow, kind of thing.
Moving on to another fae creature now!
The Banshee
So... my family has a Thing with Banshee, ngl. We have one that follows one side of the family and an elemental spirit that follows the other side. Fire and death is... unsurprisingly common in my family.
I know a personal family tale of a family friend and a cousin who saw a Banshee. The family friend or cousin (depends on who I hear the tale from lol), shouted at a wailing woman on a wall, combing her hair, so she threw the comb at him and, basically, he got a death curse from a Banshee (or marked as being The One Who Was Gonna Die idk) and died eventually.
My family is O'Brien... quite a bit actually, and is one of the five families that Banshee cry for. It's been heard for several family members in the past and, not lying, I'm not sure if my mother and I have heard a wailing woman or an owl. We have a screech owl in the trees nearby and the sod really likes screeching a lot so... yeah.
Anyway! Banshee and death! Lovely topic...
Banshee is Gaelic for "fairy woman" aka Bean Sidhe. The purpose of a Banshee is to foretell death. A Banshee attached to a family line, as is the case of the five major families of Ireland (and especially the royal O'Brien's from whom I'm descended wahoo) and portents the death of any family member by either wailing or appearing to family members or guests. Depending on which part of Ireland you hear the story the wailing of the Banshee can differ: in Kerry, the sound is lower and more pleasant like singing, in Tyrone it's like nailing boards together, and on Rathlin Island it's somewhere between a woman's wail and the sound of an owl.
This link here has an analysis of the Dullahan and Banshee in Irish history and the potential purpose of them for understanding and processing death.
The Morrigan
The Morrigan is the Phantom/Great Queen, associated with war, fate, doom, death, and victory in battle. She often appears as a crow (the badb). Whilst she isn't a fae directly connected to death like the Dullahan or Banshee, the Morrigan still has ties to death since it can be argued that she determines who lives and who dies in battle.
If the Morrigan isn't shown as a single individual, she is seen as a trio instead. The Three Morrigna. When The Morrigan is a trio, she is usually the goddesses Badb, Macha, and Nemain (or Badb, Macha, and Anand). Arguably, the Three Morrigna could have been the same goddess in different aspects. Other versions of the Three Morrigna have it as three land goddesses; Banba, Fodla, and Eriu.
Whichever of the Morrigan is the wife of The Dagda, she is associated with the Banshee and possibly, maybe, an earlier form of the Banshee of later Irish folklore.
Other fae things related to death
There is some blurring of the lines between fae and mortal when people die, with some tales using the departed souls in fae-like ways.
Such as the Cauld Lad of Gilsland who acted like a Banshee foretelling death by shivering and moeaning at the bedside of those destined to die; which, considering the Cauld supposedly was a boy who died of hypothermia, is kind of horrifying.
There's some Scottish folklore that have spirits given fae powers; like the Sluagh of the Scottish Highlands, known as the Hose of the Unforgiven Dead.
Other versions of the Banshee, Bean Nighe, washed blood-stained clothing in streams were thought to be restless spirits of mothers who had died during childbirth rather than full-fledged fae.
There's also foxes around the castle of Gormanston who would congregrate whenever the head of the family that resided there was about to die. Having your death portended by the yipping screeching of foxes is... interesting. Especially considering the Murdered Woman Scream of vixens, honestly.
There's also Shucks. These are hell hounds, devil dogs, just big ol' black dogs ala Grim from Harry Potter, that can be ill omens or treasure guardians etc. Black dogs, like black cats, kind of have a bad reputation which, I suppose, is because they're black... :/ awkward much.
Anyway, Black Dogs, or Shucks are especially prevelant in English folklore and definitely European and American folklore too. In Ireland, they're known too.
I actually have an interesting story from my mother about my great-grandmother seeing a black dog. She actually lived in Liverpool at the time so, I suppose, it's still English folklore but Irish family and an O'Brien to boot (some luck, huh). This was way back before the area was all built-up so there was a lot of open area, trees etc. She was walking up to meet one of her daughters from work and had (possibly) my maternal grandfather with her. They were walking back and saw this large black dog in the open field. It didn't speak or make sounds etc, but followed them all the way back. My maternal grandfather said he turned around and threw a brick at it, to chase it away, and the brick went clean through it.
Not at all ominous and disturbing.
Death Plants?
Of course there must be a plant of some kind associated with death. It is, incidentally, the Hawthorn tree. In irish, it is known as the Faerie Tree (Sceach Gael) because it is said to guard the entrance to the fae realm. Incidentally, it's bad luck to harm one which bodes poorly for me. It was believed that bringing hawthorn into the house would be followed by illness and death.
Meadowsweet was also another plant associated with death. It was used to make mead (ironic) and the scent of its flowers apparently caused a sleep so deep it was fatal (I don't think it was the smell of the flowers insomuch as what they were used to make). Contrary to this, in County Galways, meadowsweet could cured a person wasting away because of the influence of fae by putting it under their pillow.
Blackthorn too, is considered an ill omen and connected with death. It is linked with death, wounds/injuries, warfare and the Morrigan. The Goddess of Winter, the Cailleach strikes the ground with a blackthorn staff to mark the beginning of winter (the time when things die, basically).
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So, there you go nonnie. Lots of things about death in Irish folklore, some connections to the fae, some blurring the line between mortal and fae, and some family stories from yours truly that are going to make sleeping a challenge for me tonight!