The grammar is kind of squirrely (and probably represents an Aramaic original passed down to text). To give only one example, despite a very popular and widespread emendation, there was most likely no verb in the Greek at Mark 14:21, but the verb is supplied at Matt 26:24 (the texts of which are otherwise identical):
kalon (en) aut(i)o ei ouk egennethe ho anthropos ekeinos
kalon = good
(en) = was (found in GosMatt’s text)
aut(i)o = a prepositional third person pronoun, but in a weird case: “him” with a preposition implied. Most translations go with “for” as the equivalent English preposition, but to be blunt that’s kind of a guess, as exemplified by Green who in his literal translation took the standard “for” but in his super-literal translation he didn’t bother even trying to supply a preposition!–but placed the implied “it” there instead.
ei = if
ouk = not
egennethe = was born
ho anthropos = the person
ekeinos = this is an odd reflexive term in Greek; it’s built from a word for “there” but is used for emphasis in regard to the noun it modifies (sometimes with its own direct article, though not this time). We would say in English “that there one”! 
Or “that selfsame one”.
The final clause certainly reads then: “if not was born that there person” or “that selfsame person” or or “that very same person”.
The implication from the emphasis at the end is that the speaker is talking about a person he just recently referenced. By context, this can only mean Jesus or Judas; and almost certainly means the person being talked about in the first clause.
So if the “him” in the first clause is Judas, the second clause’s person is also (almost certainly) Judas. If the “him” in the first clause is Jesus, the second clause’s person is (almost certainly) Jesus.
Now however we get to another related use of {ekeinos}: a tool for helping authors distinguish between men when talking about two of them (especially in relation to each other). Is there another nearby use of “that very man”? Yes there is, back in the previous sentence (both in GosMatt and GosMark; also GosLuke for what it is worth although GosLuke doesn’t have either of the two clauses of the ending sentence.) “But woe to that-very man by whom the Son of Man is betrayed.”
By grammatic implication, the two “that-very” men are the same man, namely the one who betrays the Son of Man. So was the Son of Man betraying the Son of Man? Matt 26:25 “And Judas, who was betraying Him…” starts the next sentence. (Also preceding context “One of you will betray Me”.)
This however opens back up the possibility that the “him” in the first clause of the final sentence does not refer to “that-very man”, since the term is definitely used for another purpose. It could of course be used for both purposes; but since “him” has already been used once in this statement and only for the Son of Man, then the parallels of usage would suggest that “him” refers to “Him” rather than to “that-very man”.
In the final analysis the grammar could be used either way: “him” in verse 24c (and its Markan parallel) could still be Jesus or Judas, although Judas is definitely “that-very man” at the end of 24c (and GosMark’s parallel).
Fortunately all this can be settled by cultural context much more easily–and, in passing, also lends weight to an interpretation of what we ought to be expecting from Christ in regard to Judas: the saying elsewhere (such as in Job) is a call for pity for that man of whom it would have been better had he not been born. And that fits the term being used for “wail” or “woe” in all three Synoptics here: it means “lament” in pity.
That means the saying is in fact about Judas in both its clauses. But it isn’t a curse of hopelessness for Judas: it’s a cry for pity for Judas. Jesus instructs His other disciples (and us too by extension) to be sorrowing in pity for Judas; to be hopefully loving him even in our grief for him. (True, Peter at least doesn’t seem to be doing this later in Acts; but Peter messes up a few times in other regards in those same opening chapters regarding his ministry and has to be slapped up and down a bit. 
This could be one of those times as well. At least Matthew in his unique Gospel material works hard at soliciting pity for the traitor–maybe having lived his life as a traitor to Israel before his apostolic call, he was able to pity Judas more.)
This could have independent (if subtle) confirmation from GosJohn, too: theologians have long wondered why “be loving one another” was supposed to be a new commandment. This Easter while devotionally reading the material, I noticed for the first time that Jesus tends to say this in proximity to references to Judas and his coming betrayal!
Loving our greatest enemies is presented elsewhere by Christ (especially in the Synoptic preaching material) as being the greatest fulfillment of the Law to love our neighbor; in the form “you have heard it said, but I am saying to you”, Jesus is practically re-giving the commandment in a new scope. I think it makes sense for Him to be challenging (and requiring!) His disciples and apostles to be loving one another even when “one another” includes someone like Judas Iscariot.
By this indeed “men shall know you are My disciples: if you are loving one another.”
What faithful disciples of a teacher do not ideally love one another?! But, which teacher has ever gone so far as Christ in insisting on loving the worst traitors as He has loved us when we were still sinners?
No greater love is there than this, that a man will lay down his life for his friend, Jesus says. Yet Jesus also says that this is entirely normal among the nations, and that loving those who love us is of no special weight; and St. Paul agrees that for a good man someone may dare even to die. But “this is love” that while we were still sinners Christ died for us.
And Jesus, at the moment of betrayal, still calls Judas: “Friend.”
Personally I don’t think sin shall permanently ravage God’s purposes for people.