Please follow the train of thought that Jesus threads through the Book of John to the end. During a discussion about faith with some Jews, Jesus said, "All that the Father gives me will come to me" (John 6:37) - From this text we understand that all that the Father gives to the Son will come to faith in him. It does not read "some" of those given by the Father will come to faith but reads "all" of those the Father has given the Son will come to faith in Him. Note that it also teaches that the giving to the Son precedes their believing in Him. Lets make some other connections from the Gospel of John here ....
Please notice how this text in John 6 also relates directly to a passage by the same Apostle in John 17 in Jesus' High Priestly prayer. Jesus uses the same phrase: "those the Father has GIVEN ME" when he says "I am praying for them. I am not praying for the world but for those whom you have GIVEN ME, for they are yours" (John 17:9) So He makes a clear distinction of those He prays for and those He does not before going to the cross for them .... and of these same people in verse 19 Jesus prays "And for their sake I consecrate myself, that they also may be sanctified in truth." That is incredible ... He sanctifies Himself so all those the Father has GIVEN HIM will also be sanctified ... and in verses 20 & 24 he establishes that he further is speaking NOT ONLY of the immediate disciples but of others who the father has "given him" (v 24) who hear the apostles word. There is that patten of language of "given me" spoken again about those outside his immediate circle. This exegetically demonstrates the truth of particular redemption, especially since Jesus is praying for all those the Father has given him just prior to going to the cross to sanctify them.
In sum, Jesus sanctified himself for "all that the Father gave him" that they they also might be sanctified. It does not get any clearer than that. (John 17:9, 19, 20 & 24)
Who is the "they" that Jesus "sanctifies" in John 17:19? (see v. 9 & 24)
Is the "sanctification" of "those the Father has given him" part of Jesus redemptive work? Or is it non-redemptive?
If Christ begins our sanctification, will He infallibly bring it to pass? (See John 6:37b)
Understanding 1 John 2:2 by John Samson
Universal Redemption Must be Denied by Jonathan Edwards
Particular Redmeption (MP3 Series) by Albert N. Martin
Exposition of John 17:17-19 On Particular Redemption -Part I (MP3) by Art Azurdia
Particular Redemption - 2 Corinthians 6:1-18 (MP3) by Sinclair B Ferguson