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So Judah and Gene suggested some spice...so here goes.
A remnant is "what remains of any entity after most of it is used or destroyed" (McComiskey). In the Scripture, the remnant is what remains of the entity of Israel, sometimes specifically referring to the remains of the House of Israel (as opposed to the House of Judah).
Christians have noted that James, in Acts 15, applies such remnant passages to the gentiles:
"...he cites Amos as the scriptural basis for his position. The quote is in fact a conflation of Amos 9 and other texts, such as Jeremiah 12:16 and Zechariah 2:11..." Are Christians the 'Aliens Who Live in Your Midst'? Torah and the Origins of Christian Ethics in Acts 10-15 by John Perry
"James's point is not just about this one passage from Amos; rather; this passage reflects what the prophets teach in general, or what the book of the Prophets as a whole teaches. Other texts could be noted (Zech. 2:11; 8:22; Isa. 2:2; 45:20-23; Hos. 3:4-5; Jer. 12:15-16)." Acts: Baker Exegetical Commentary by Darrell L. Bock
This is weird, right? Why was James associating these remnant passages to the gentiles as though the gentiles were the remnant of the House of Israel? But it gets weirder...
Both Peter and Paul seem to apply to gentiles the Hosea prophecy that promised the restoration of the all but destroyed House of Israel:
1 Peter 2:9
9 But you are a chosen people, a royal priesthood, a holy nation, God’s special possession, that you may declare the praises of him who called you out of darkness into his wonderful light. 10 Once you were not a people, but now you are the people of God; once you had not received mercy, but now you have received mercy.
23 What if he did this to make the riches of his glory known to the objects of his mercy, whom he prepared in advance for glory— 24 even us, whom he also called, not only from the Jews but also from the Gentiles? 25 As he says in Hosea:
“I will call them ‘my people’ who are not my people;
and I will call her ‘my loved one’ who is not my loved one,”
“In the very place where it was said to them,
‘You are not my people,’
there they will be called ‘children of the living God.’”
ON TO THE QUESTION:
Why were these apostles (James, Peter, Paul) applying to gentiles passages that promised the restoration of the House of Israel?