IMHO John 10:16 is a kingdom statement and IMHO is a reference to prophecy of Ezek 37:24-28
Then said God, Call his name Loammi: for ye are not my people, and I will not be your God. Hosea 1:9
Who is not the people of God? In the year 5 BC were they still not the people of God?
Hosea 1:10 Yet the number of the children of Israel shall be as the sand of the sea, which cannot be measured nor numbered; and it shall come to pass, that in the place where it was said unto them, Ye are not my people, there it shall be said unto them, Ye are the sons of the living God.
Who is, them? How do the same, them, become the sons of the living God?
;
Isaiah 1:1
Isa 1:1 The vision of Isaiah the son of Amoz, which he saw concerning Judah and Jerusalem in the days of Uzziah, Jotham, Ahaz, [and] Hezekiah, kings of Judah.
Hosea 1:1
Ho 1:1 The word of the LORD that came unto Hosea, the son of Beeri, in the days of Uzziah, Jotham, Ahaz, [and] Hezekiah, kings of Judah, and in the days of Jeroboam the son of Joash, king of Israel.
The LORD knows how to address the two houses of Israel, Judah and Ephraim. They are the same people some 700 years later and one can determine that the Northern family of ten tribes still, after all these years, worshiped Jehovah as their God, even though he said "ye are not my people." We can be sure of this because the first missionary journey of the great apostle Paul found him preaching in synagogues in the regions where they abode in his days, Asia minor. Peter wrote his epistles to them and addressed them, not as sons of God, but as strangers.
1Pe 1:1 Peter, an apostle of Jesus Christ, to the strangers scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia, (these are all provinces in Asia Minor)
2Pe 3:1 This second epistle, beloved, I now write unto you; in both which I stir up your pure minds by way of remembrance:
1Pe 2:9 But ye are
a chosen generation, a royal priesthood,
an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light: (you will see how important this generation is in God's scheme of things when I make my post about the generation of Jesus Christ)
As a side note, Paul, writing his 13 epistles to the gentiles never one time even hinted that we, members of the church of Jesus Christ, are priests. He did not use the word priests or priesthood in any of his epistles as he gave us the great doctrines of the church in this age.That is significant.
But how do they become "children of the living God" like is prophesied in Hosea? If one becomes a child of someone, he must be born into his family. This letter then is in a broader sense than just the church of Jesus Christ, of which all who were born again at this time are members. These members of Israels race will still be around and many of these things will yet apply to Israel after the church is taken.
These are the folk that are in view here:
Rom 9:22 What if God, willing to shew his wrath, and to make his power known, endured with much longsuffering the vessels of wrath fitted to destruction:
23 And that he might make known the riches of his glory on the vessels of mercy, which he had afore prepared unto glory,
24 Even us, whom he hath called, not of the Jews only, but also of the Gentiles?
25 As he saith also in Osee, I will call them my people, which were not my people; and her beloved, which was not beloved.
26 And it shall come to pass, that in the place where it was said unto them, Ye are not my people; there shall they be called the children of the living God.
27 Esaias also crieth concerning Israel, Though the number of the children of Israel be as the sand of the sea, a remnant shall be saved:
28 For he will finish the work, and cut it short in righteousness: because a short work will the Lord make upon the earth.
29 And as Esaias said before, Except the Lord of Sabaoth had left us a seed, we had been as Sodoma, and been made like unto Gomorrha.
God had mercy on Judah but did not have mercy on Israel, though later God said that the sins of Judah were greater than the sins of Israel. In this age after the cross work of Christ the believers of Israel became the remnant, the very small seed, the children of God through the new birth, and as great as it is it is not the end of the story for this nation. The word of the Lord gives many prophesies concerning this people that one cannot learn by reading the OT scriptures.
1Pe 1:18 Forasmuch as ye know that ye were not redeemed with corruptible things, as silver and gold, from your vain conversation received by tradition from your fathers;
19 But with the precious blood of Christ, as of a lamb without blemish and without spot:
20 Who verily was foreordained before the foundation of the world, but was manifest
in these last times for you,
21 Who by him do believe in God, that raised him up from the dead, and gave him glory; that your faith and hope might be in God.
22 Seeing ye have purified your souls in obeying the truth through the Spirit unto unfeigned love of the brethren, see that ye love one another with a pure heart fervently:
23
Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever.
24 For all flesh is as grass, and all the glory of man as the flower of grass. The grass withereth, and the flower thereof falleth away:
25 But
the word of the Lord endureth for ever. And this is the word which
by the gospel is preached unto you.
The word of the LORD is a person when this title is given to him.
One cannot give much detail on these forums because of the limitation, but I give these verses for comparison and thought. No one might agree with my conclusions but every word is important in the scriptures.
Rom 11:I say then, Hath God cast away his people? God forbid. For I also am an Israelite, of the seed of Abraham, of the tribe of Benjamin.
2 God hath not cast away his people which he foreknew. Wot ye not what the scripture saith of Elias? how he maketh intercession to God against Israel saying,
3 Lord, they have killed thy prophets, and digged down thine altars; and I am left alone, and they seek my life.
4 But what saith the answer of God unto him? I have reserved to myself seven thousand men, who have not bowed the knee to the image of Baal.
5 Even so then
at this present time (58 AD) also there is a remnant according to the election of grace.
25 For I would not, brethren, that ye should be ignorant of this mystery, lest ye should be wise in your own conceits; that blindness in part is happened to Israel, until the fulness of the Gentiles be come in.
26 And so
all Israel shall be saved: as it is written, T
here shall come out of Sion the Deliverer, and shall turn away ungodliness from Jacob:
27 For this is my covenant unto them, when I shall take away their sins.
The mystery is not verse 26 because it is an OT quote and prophesy that is plainly understood. The mystery is verse 25 that says the judicial blindness of Israel will end when the gentiles have filled the house and the church is complete.
There will be no more remnant doctrine of Israel, going forward, because at the end of this all who are left after God's baptism of fire prophesied by John the Baptist, which will be few, will all be saved and his physical and spiritual promises will be realized..