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It is possible to say what time it is for someone (it's 1 AM here): so why can't we construct a B series for them? Is it reasonable to do so, and what would the word for the series be?
There is no such time after death. Does an event end even if there is no after it?
I am asking because I want to know in what sense e.g. Blanchot means there is
an arrival of death which never arrives and never happens to me
an arrival of death which never arrives and never happens to me
This is very much the subject of Derrida's book Aporias.
As the filaments of consciousness or being disintegrate can there be any moment at which being stops. Indeed, how can one not be, or transition from an existing Being to a non-existing non-Being, (since the being cannot do non-being). The orthodox analysis of being has to accept unfamiliar gradations of being which might be stepped through in order to handle this novel subject area between being and non-being -- the aporia of death.
The B series:
From a second point of view, one can order events according to a different series of temporal positions by way of two-term relations which are asymmetric, irreflexive and transitive: "comes before" (or precedes) and "comes after" (or follows) [1]
So, the B series is more concerned with placing events into a causal chain of events, not based on pastness, presentness, or futureness. whereas the A series assigns these qualities to events based on the 'present' as a point reference. the difference between the two is similar in many respect to the difference between a subjective and objective view.
In terms of your question, the B series is tenseless. so the statement, 'It's 1AM here' is not a B series statement, since it contains (implicitly) a reference to 'now'. I think its perfectly possible to construct a B series of someone, provided that it is objective, so instead of 'Bill is here now' you'd say 'on September 9th at 10PM bill was here' (obviously it would be much better if you could say it in some kind language that didn't rely on tenses to be coherent.)
not sure that theres a specific word for that kind of series though...
For the second question,
I believe Blanchot is referring to the idea that death and consciousness cannot coincide. Thus, Death cannot happen 'to' us, we cannot experience it [2], because experience is, by its nature, life.
Similarly, for death to 'arrive' it must present itself to our awareness (we must become conscious of it), but this is impossible. Imagine your mind is a pitch black room with a torch suspended from a string in the centre. The beam of the torch is your awareness and the dark parts are your unconscious. The torch is free to point wherever it likes,but no matter which way it points, from its perspective the entire room is brightly lit. So we cannot become conscious of what we are unconscious of, and death is by its nature a severe kind of unconsciousness. Just as the blackness of the room cannot become present to the beam of the torch, so death cannot become present to your awareness.
Hence, the arrival of death which never arrives and never happens to me.
As to Blanchot, the endless "arrival" seems a version of Zeno's paradox. As Robert notes, "my death" and "my consciousness" cannot precisely coincide, the former defined as the negation of the latter. The trajectory of "me" acts like a limit in calculus to the trajectory of the precise "moment of death."
Thus, in Zeno's timeless world, "I myself" never die! But, alas, back in the A Series, death happens to "him," who "was me."
Your B series problem has a definitive answer, I suspect. But I'm not up to speed. I believe the problem lies in "here." Of course, a B Series can observe "It was 1 AM for Mr. Math in Mathtown right before this clock struck 1:01." But once "here" or "now" enter in, references to simultaneity break down.
