2 Kings 17 describes the destruction and captivity of the Northern Kingdom of Israel in 722 BCE:
In the ninth year of Hoshea, the king of Assyria captured Samaria, and he carried the Israelites away to Assyria and placed them in Halah, and on the Habor, the river of Gozan, and in the cities of the Medes….Therefore the LORD was very angry with Israel and removed them out of his sight. None was left but the tribe of Judah only….And the LORD rejected all the descendants of Israel and afflicted them and gave them into the hand of plunderers, until he had cast them out of his sight….The LORD removed Israel out of his sight, as he had spoken by all his servants the prophets. So Israel was exiled from their own land to Assyria until this day. And the king of Assyria brought people from Babylon, Cuthah, Avva, Hamath, and Sepharvaim, and placed them in the cities of Samaria instead of the people of Israel. And they took possession of Samaria and lived in its cities. (2 Kgs 17:6, 18, 20, 23-24)
I’m going to offer three biblical reasons why this Southern portrayal of Israel’s complete destruction and exile should not be taken at face value.
1. The wording of 2 Kgs 17:23b and 25:21b is nearly identical:
וַיִּגֶל יִשְׂרָאֵל מֵעַל אַדְמָתוֹ אַשּׁוּרָה עַד הַיּוֹם הַזֶּה
17:23b: “So Israel was exiled from its land to Asshur, to the present day.”
וַיִּגֶל יְהוּדָה מֵעַל אַדְמָתוֹ
25:21b: “So Judah was exiled from its land.”
Yet, 2 Kgs 25 is clear in the verses preceding and following this contention that there were Judahites left in the land after 587 BCE (vv 12, 22-26). (This contention is supported by archeological evidence, but that is beyond the scope of this argument.) This gives us textual warrant to doubt Dtr’s contention that all the ethnic Israelites were deported from Samaria.
2. The Chronicler’s emphasis on kol yisra’el (“all Israel”; over 40x) in the Persian period makes little sense as a vision of restoration if ten of the twelve tribes are irretrievably lost in the East. Similarly, the DtrH’s emphasis on the inclusion of the Northern tribes makes little sense unless Judah integrated some Northern refugees after 722. Nowhere in scripture, archeology or other historical record is there any evidence of a Northern return from Assyrian captivity.
3. The preservation of at least some members of the Northern tribes is confirmed by Luke 2:36, which records that the prophetess Anna is of the tribe of Asher. Even if this claim does not seem credible to modern historians, it indicates that some Jews in the first century CE at least claimed descent from the Northern tribes, a claim that their contemporaries considered plausible.
For these reasons, I think we can safely say that not all the ten tribes were lost, at least by the period described in Ezra-Nehemiah. Whether they were integrated into Judah prior to 587, or remained in the land alongside the imported peoples, Israelites remained in the land and continued Yahwistic worship, albeit in a form that was not acceptable to the Southern perspectives preserved in scripture.
I’ve tried to show from the text of scripture that this is so. I don’t think this undermines the true meaning of 2 Kings 17, which is that the Assyrian invasion was brought on by syncretism and other disobedience to God’s Law. By comparing scripture with other scripture (the whole counsel of God) and what we know from history, we can discern the true theological meaning of this individual chapter.
 This explains the presence of strongly pro-Judah and lesser pro-Northern strains in the DtrH, especially Judges. Judges values the primacy of Judah (Jdg 1:2, 19) and points to the needs for a Judahite-king (David), but also values the inclusion of Benjamin (Jdg 20-21) and the leadership of the prominent Northern clans (Deborah, Barak, Gideon, Samson, etc.).