Perhaps longeval, also spelled longaeval or longæval, might serve. Per the OED, it means long-lived or long-lasting. Their first citation provided is from 1597.
This word also occurs as a substantive. For example, the pre-Flood patriarchs from the Old Testament were held to be longevals.
Tolkien and Lewis used the term in their writings. For example, from Tolkien’s Letter #245 we read that
The Elves were sufficiently longeval to be called by Man ‘immortal’. But they were not unageing
or unwearying. Their own tradition was that they were confined to the limits of this world (in
space and time), even if they died, and would continue in some form to exist in it until ‘the end
of the world’.
That comes closest to what you’re talking about, although some qualification is required to distinguish the notion of being long-lived from being undying.
Then again, you can’t actually “kill” an elf in Tolkien’s Legendarium. Yes, you can take from them their life — but only for a while. They are part of this world, and their fates are bound to it. Their span is that of the world itself; beyond, none save perhaps Manwë alone can say. They cannot leave the world through a mortal death, for mortal they are not, and slain they will ever return, whether a hundred years from now or a thousand or ten times that, returning in their own flesh again and again and again till the world’s ending. Though Sauron slew Galadriel’s brother Finrod Felagund while the king was defending Beren, The Silmarillion tells us that he lies not in his grave, but that he walks with his father Finarfin beneath the trees in Eldamar, and the Lay of Leithian records that
while Felagund laughs beneath the trees
in Valinor, and comes no more
to this grey world of tears and war.
So perhaps that longeval would be close enough, although it is not strictly speaking undying.
See also this question’s answers for other ideas: Everlasting, Sempiternal, Æviternal, Omniëssent, and Omnitemporal.