That is a fine question.
In a recent Henle edition that I have, two versions of this Nocturne are published one after the other. There are differencies, but mainly in notation. The differences I'm thinking of is a # in fourth and third last bar (at the end), a sign that is put in between crochets (#) which I only can understand as "it's up to you, dear musician, you can play it with or without". And indeed, it is playable with or without, but musically it gives a slightly other difference in meaning. This nocturne, as many of the nocturnes, has a certain tristesse, melancoly, to it. Since it's a 'Posthumous' one, I can't avoid thinking at Chopin's death, or that he considered it somewhat 'worthless' since it only has been published after his death; it could be that he wasn't totally satisfied with the piece, he maybe worked a long time on it, put it aside, reworked, put it aside, never got totally satisfied with it and finally died. So there probably had to be dealt with what we could call a very advanced sketch, a work far in progress but never truly finished or edited... But inevitably, there is this subjective death in it. I do not pretend that this Nocturne speaks about death, I don't think it was Chopin's intention to 'speak' about death, at least not in this particular Nocturne. Now I would like to make a little side step to a Walz of Chopin, Walz number 34/2. It is a deeply sad piece of music. So sad, so pessimistic, so tragical, fatal, so black. Even within the piece itself there is this sort of "non-music" and it is ending totally "down", "at the bottom of everything", nothing expanding, not something 'universe'-like, but deep in the ground, where there's no light anymore, no sound. Even in this Walz we can here some attempts to be joyfull, but they fail every time. And then suddenly this very sad "Do", that change of key, so "out of hope". Again an attempt for happiness but nope, nothing to do. The sadness and hopelessnes is the winner... I do not think that this Walz at one point can be played like a Walz, it is never a Walz and it never becomes one. Only the introduction could eventually be seen as attempt to become a Walz. In the Nocturne Posthumous, I can also hear sadness, less 'thick liquid' than in the Walz, but there are, surely at the end with these I don't know the correct word in English three rolls of note (arpeggio's ?) up and downwards, that give a lot of air in the end. But first things first. It is lento, starts with a kind of heavy, prologue, not really an introduction but really a moodsetter. Makes me think of 'the end', it is also fatal. And than strangely, a repetition of that intro. It should be played differently, but in such a way that it is not a very different thing, but just an other attempt that gives no immediate result, no 'answer', that tells nothing about what will follow. Then things go slowly, higher... and higher... but... - what do we expect ? - the first part swoons down, goes deep down, with a cramp, to end, well not end totally but definitely change. We could go in a lot more detail for this first part but let's skip to the 'at first hearing' nice second part. Almost delightful, one could almost dance to this part, "there is some fun once in a while, but is this really the fun we should believe in and stick to ?". It is an interrupting fun, moody, is it trustworthy ?, weren't we kind of down and dreamy in the first part, I'd rather prefer (what is typical for a depression) stick to that mood, I was better in and over there... Now the delightfull part fades away, in those repetition of triolets', second part dies away and then lifts of away to end with, in my opinion, one of the most light notes in pianoliterature. "Light" in the meaning of light like a far away tinkling star, but also very light as opposed to heavy and not infinitely ppp but just that audible like an impossible marriage of velvet and crystal... Ah there again, that theme, the repetition of that theme, we'll play it a little bit more piano than the first time, to accentuate the factor of 'reminiscence', maybe it is talking about regrets. Finally, the three - allow me to call it - rolls to end in the last four bars with what is clearly - and now we come to the topic - different from one edition to the other. The (#). This piece, in opposition to the Walz, doesn't end in total air- and blackness, but leaves a little air, and puts a slightly smiling end to the experience. One can die with a slight smile on its face. In one version you 'could' (you're not obliged) play the # immediately after that last very 'delicatissimo' roll and let slip in positiveness right away, then there is a more totally positive end. But that could be in my eyes a little grotesque. I prefer to play the # only in the last bar, so you let 'hear' delicately, subtly a glance of positiviness, it just changes mood so little, less drastical then the first option, and let slip in positiveness only at the utter and very end.
So up to you to choose !
Good luck.