Death was not hired to be an entertainer. They were hired to be an assistant or something. It was never listed on their job description that they needed to braid hair, and technically they knew how to do it--they themselves usually had braided hair--but it seems that, out of some sort of consideration, they also left their own hair loose this day. Well, unlike Dalia's hair, it was almost completely loose, albeit with a few ties towards the center in the back. The quality of the hair itself probably makes up for the lack of style, with its pure white color and the occasional band of light shifting with the light source around them. 
Otherwise, for them, it's just a normal day. At no time has Death wallowed in a feeling such as boredom or loneliness. Even in a castle devoid of the many tasks there used to be, they can find things to do, and find things to do is what they do. In fact, even though they're dressed as usual--suit, tie, top hat, and all--they don't mind cleaning rooms if it comes to that. Perhaps unhelpfully, they rarely enter the room where Dalia is, that room at least having been cleaned many times. 

Not to be rude, Dalia, but I doubt you have a good impression on anyo--*sees Death staring and hides*.

~

They are within a hallway adjacent to the one that led to her current location. For someone who seems so slow, they walk surprisingly fast. And like a phantom, which they somewhat resemble, it's usually nearly impossible to find them, but for career purposes, they let their presence be out in the open for now. 
It's questionable why Dalia thinks of Death first for conversing. They usually don't talk at all. 

Death pauses where they are as soon as they hear any sort of noise. Even though the castle is mostly quiet by now, their instinct always points them towards being attentive towards any sort of noise, not to mention when a familiar voice is speaking to them. 
However, since she didn't exactly establish a firm telepathic link, they would have to do so to respond. Instead, they just reckon that getting back to the throne room is the best response possible and, never to disappoint their employer, they're in the throne room. Yes, immediately.
As soon as they're there, they place their right hand onto their chest and bow to Dalia with all reverence.  

Death does straighten, but they keep their gaze somewhat aligned with the ground. That's what it looks like, anyways, but in truth, they're gauging her expression and other hints as to what she wants them to do. Specifically, they're reading her to see if she wants them to speak or to remain in silence. 
Remaining in silence is the safer option, since she's the one who beckoned them here and thus shouldn't need a reminder of so. Even so, it doesn't hurt to check. 

Yay, as expected.
Death's mouth curls upwards slightly on both sides, kind of like a cat. "'Very well, madam. Thank you for asking," they say, before adding their usual narration gimmick at the end.

"'Yes. I am never particularly appealed by a trend of that sort,' answers Death." They do so in a very polite manner, as per usual, the little cat-like smile on their face staying there as if in wait.

They contemplate that for about one second and, being a fast thinker, respond: "'My apologies, m'lady, but being one accustomed to solitude and supposed tedium, I am afraid I am not qualified to answer that question,' Death responds apologetically. 'Would that perhaps be your perception?'"

As a servant of just anyone working for someone else, it's a general rule of thumb that one shouldn't wait for that someone else to make it completely and specifically clear that they want you to do something. In this case, Dalia has already made it completely clear that there is something--or someone--she wants them to bring back to her. Then, it would be foolish for Death to continue making the goddess--their goddess--wait. 
Death is no fool; far from it, in fact. They bring their hands together in a clearly submissive gesture and swiftly kneel on one knee, that cat-like smile still there. Your wish is my command, m'lady.

Yes. How did they know? Hmmm...maybe they have their ways of knowing, or maybe they just remembered, somehow. 
It's notable they've switched to telepathy, as is the case every time when they perceive it's better off avoiding their gimmick.

Please do not worry. I shall attempt to finish the task as promptly as possible and without delay, states Death regardless of whether that was sarcastic or not. You're not exactly supposed to interpret something like that in their kind of role. Regardless, they pause slightly. That much is visible from their face, though the rest is just the usual unnerving sort of calmness mixed in with an equally unnerving smile.
...excuse me for asking this, please, but if Sir Allen is somehow unwilling to return...do you have specific orders upon that topic?

Well, so much for them asking just to make sure. Not that they didn't expect that answer, unfortunately.
Understood. They slightly emphasize the gesture they made from earlier, possibly now expecting to be excused.
 

They bow one last time and then step out, the first few steps in reverse step before they turn around carefully and walk away, their footsteps completely silent.
Uh, let's just say the doors are open, so they don't need to open them to exit the room. 
It's only once their silhouette cannot be directly seen by the goddess that Death stops in their steps to contemplate where they should start in this mission. Of course, they do remember to step to the side of the hallway in case anyone passes by--they never seem to do so--but it's good to keep the mannerisms habitual. 

(How did you want to do this? I'm guessing no one's gonna go along with Death, so just a big solo POV on my part? And we don't need to tell Rune that this is happening, so we don't need a thread switch of any kind, correct?)

Death is real prompt about it, but the narrator isn't. Hope Dalia isn’t dead of boredom yet.

(Lol long and dramatic POV here we gooo)

They are going into the affair with absolutely no expectations other than the one that states they will succeed. They do not expect the task to possess any level of difficulty. They do not particularly expect there to be specific obstacles. Their only expectation is that their efforts will come to fruition and they will finish their task. There is no other particular related thought in that matter.
That is their mindset in order to cast their emotions aside in a matter that was already not very related to them in the first place. It is something to be done on their part. That is all. They do not have any attachment, or any disappointment, or any worries...or even any enthusiasm for the task, really.
It is just a task. That is all there is to it.
Even if it is a task, there is no visible change to Death by the time they finally start walking again, their pace as languid as usual, though perhaps their gaze is steelier than the usual. Just by a bit, perhaps. And then their silhouette starts fading from the castle, until it is as if they did not exist in it in the first place.
Funnily enough, their form reappears in the sky somewhere: In a place that somehow seems devoid of a light source yet thoroughly bright, with it being enough to illuminate even Death’s palest features to the point of indistinguishability--but within less than a second, all the brightness seems to vanish, giving way completely to an undefeatable darkness that vanquishes all brightness on Death’s forms as much as the light preceding it had illuminated it and made it practically invisible.
Indeed, someone normal would probably obtain a seizure without being predisposed to one just from being in this place for even a few seconds, but the youth remains completely unaffected. They stare into the distance through many revolutions of the darkness and brightness, shifting their gaze from one fixated point to another, their mouth slightly moving as if trying to mimic someone else’s speech.
Through every repeat, the sense of timelessness intensifies. It would feel as if everything is set in stone--as if anyone who enters this sort of place would no longer have the option to leave--but with every moment, the corners of Death’s mouth lift again. This time, it is no longer like the sneer of a cat, but rather the uplifting of a child’s mouth as he realizes that he has found something that he never found before. Perhaps the only unnerving quality now is that the only hint of delight in any of their features is precisely around their mouth and nowhere else.
Finally, a giggle escapes from the youth, though for some reason there is absolutely no happiness in their laughter: 
“...ah, you who put up the barrier...you really are very careful,” they murmur with careful words of their own. “Really, really careful. You were really afraid, were you not? That there would be someone who could easily sense the inhabitants within…come to think of it, I wonder where that fear sources from…”
“...but did you think of this giant flaw that will always theoretically be formed?” Death’s mouth curls up a bit more. “As Mr. Conan Doyle wrote, ‘Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.’ As such, as long as the one being searched for is neither one within the world of the dead nor on the boundary between the dead and alive, then undeniably, he is an alive individual who lives within a place no one can sense. Is that not the only possibility, however improbable?”
Their eyes widen, the color of both eyes penetrated by both light and darkness, and they proclaim: “I have found you, sir.” 
With that, their figure disappears from the strange place, the shape of their silhouette melting back into reality. By the time this occurs, Rune’s domain has an intruder. Mockingly translucent, Death’s eyes survey the drawbridge they never crossed that they happen to have spawned near. They run a gloved hand over the upper beam with a curious glint in their eyes. The moment does not last long; they start for the rest of the domain tranquilly soon enough, their pace unhurried and languorous.
In fact, Death practically puts themselves on a tour through the domain. They have extremely good inferences as to where the one they are seeking is, but they are no particular rush. Of course, they do not walk everywhere--they use a mix of that and some variation of flight teleportation--but they take their time surveying the inhabitants within the domain and the structure of the place itself. They take care not to take too long due to the nature of their orders, but they do have considerations that Dalia would likely only have under very specific circumstances.
Now...where could Allen be? The forest and mountain seem unlikely places due to the canyon. The library? The kitchen? The gardens? The courtyard? The room? Certainly Allen did not turn into a fish to swim in the pond and the stream.

A soft hammering upon the door separating Allen's internal, eternal world from the rest shatters the glassy barrier between the two domains, slowly becoming more and more apparent. 
"Allen?" comes a voice. It sounds like Rune's. "Sorry for bothering you, but may I come in?"

(Disclaimer: No stealing of characters was involved in the making of this post.)

A moment, maybe of waiting or of hesitation, and then the first indicator that the speaker is, in fact, not Rune, appears, a wisp of white. Then the owner of the startling white hair ghosts into the room, their hand brushing the side of the door before they retract it to a position behind their back again. 
This is, of course, a stranger and, obviously, not Rune. This is someone who wavers between the boundaries of "boy" and "man;" someone who shines a brilliant and innocent smile at Allen as if he has known the other for all of his life and Allen has known him for all of his life...and doesn't speak.