Does God say Israel will Not be Saved?

Short answer

The "not said" in both 2 Kings 14:27 and Isa 45:19b must be evaluated in context of the preceding verse (2 Kings 14:26 and Isa 45:19a). Both have to do with rhetoric, not long-term promise for the remnant of Israel post OT (end of 3rd century BC).

• 2 Kings 14:26-27 (NLT) says:

  ²⁶ For the Lord saw the bitter suffering of everyone in Israel, and that there was no one in Israel, slave or free, to help them. ²⁷ And because the Lord had not said he would blot out the name of Israel completely, he used Jeroboam II, the son of Jehoash, to save them.

  Here, "not said" simply means that the Lord still had patience for the northern Kingdom, although the Lord's patience did run out by Hosea's time (see John Gill's commentary).

• Isa 45:19 (NLT) says:

  I publicly proclaim bold promises. I do not whisper obscurities in some dark corner [how one would consult an idol, cf v. 16)]. I would not have told the people of Israel to seek me if I could not be found. I, the Lord, speak only what is true and declare only what is right.

  Here, "not said" simply serves to clarify the manner in which Israel's God speaks (through inspired intelligible words spoken by a prophet in clear daylight) in contrast to how some heathen oracles work: from the dark recess of a cavern (see Clarke's commentary).

Therefore, the overall import of Isa 45 (future eternal salvation of Israel and the world) is not connected with both "not said" verses.

Long answer

That God kept his OT promises to Israel can be easily shown from Jesus's role as the promised Messiah of the nation of Israel (Messiah = God's anointed deliverer), among his other roles that are not pertinent to this answer (such as his role as the Lamb of God, light of the world, good shepherd, defeater of death, fulfiller of the Mosaic covenant, etc.).

This answer tries to show how Jesus fulfilled the promises mentioned in Isa 45.

OT Context

We first need to read Isa 45:17 and Isa 45:19 in the context of Isa 45:14:19 (the "promise") which in turn is part of the whole of Isaiah 45 which is sandwiched between 2 passages (vv. 1-13) and (vv. 20-25). Here's the summary of the passages of Isaiah 45:

1. the "down payment" (vv. 1-13): how God provided initial deliverance through Cyrus
2. the "promise" (vv. 14-19):
   • that Israel will be saved eternally (v.17a), thus Cyrus's deliverance was only a "down payment" since later on Israel was to suffer the shame of Roman oppression
   • no longer suffering shame (v. 17b), and in fact will rule over other nations including Egypt, the previous master! (v. 14)
3. the "instruction" (vv. 20-21): how God encouraged all exiled Israel to take advantage of Cyrus's repatriation program to the land of their ancestor, in other words saying that God authorized it, no longer they need to wait or consult other gods through their idols
4. the "prophecy" for both Israel and Gentiles (vv. 22-25):
   • In fact, the world (other nations) should look to God delivering Israel as a prototype of the later worldwide deliverance (through Jesus Christ) (vv. 22-23)
   • vv 24-25 the focus is back on Israel promising "all the generations of Israel" will be justified (this is probably the basis of Paul's wondering in Rom 9-11 why empirically he noticed that most of the Jews rejected Jesus if God had promised all the generations of Israel will be justified?)

NT Context

To the contemporaries of Jesus, who were the remnant of Israel (including the later generations of those first repatriated under Cyrus back to the Land), they were all waiting for the fulfillment of God's promises in Isa 45.

Here's how Jesus fulfilled them:

• v. 17a: eternal salvation: Jesus as the fulfillment of the Davidic covenant rules over the Kingdom of God which is open (through the narrow gate) to all Israel who believe in Jesus
• v. 17b: end of shame: the "shame" at the time is about the defeat of Israel's God by other nations' gods since in the ancient mindset it's the god behind a nation who wins/loses. We can easily imagine an Israelite's chagrin when humiliated in exile by a Babylonian or when the Roman god was paraded around Jerusalem by the much more powerful Roman military. For those who believe in Jesus, they realize that not only the gods behind other nations have been dispossessed after Jesus's resurrection (Col 2:15), but in fact they were created through him in the first place (Col 1:6b)! Shame was removed because God had finally acted definitively, victoriously, and permanently.
• v. 14: rule over other nations: In Jesus all Gentiles from other nations say "Surely God is in you, and there is no other, no god besides him."
• v. 22-23: Gentiles will also be saved through Israel's God: simple fact of billions of Christians have been saved through Jesus
• v. 25: all generations of Israel shall be justified: this I think is connected to a future fulfillment as many righteous members of the Judaism religion have yet to be justified through Jesus (so I take position #1 of Nathaniel's great answer).