Why did God allow the Israelites to be captured or enslaved in the Old Testament?

Answer 1

When the nation of Israel turned away from God then He allowed them to be conquered by other nations.

Israel had the choice, to obey God and be blessed or disobey God and be cursed:

Deuteronomy 11:26-28 "Today I am giving you the choice between a blessing and a curse---

a blessing, if you obey the commands of the LORD your God that I am giving you today; but a curse, if you disobey these commands and turn away to worship other gods that you have never worshiped before

Israel disobeyed God:

Judges 2:11 - 14 Then the people of Israel sinned against the LORD and began to serve the Baals.

They stopped worshiping the LORD, the God of their ancestors, the God who had brought them out of Egypt, and they began to worship other gods, the gods of the peoples around them. They bowed down to them and made the LORD angry. They stopped worshiping the LORD and served the Baals and the Astartes. And so the LORD became furious with Israel and let raiders attack and rob them. He let the enemies all around overpower them, and the Israelites could no longer protect themselves.

Answer 2

The slavery in Egypt: The Torah states that Pharaoh claimed that the high Israelite birth-rate could pose a potential threat (Exodus ch.1).On a spiritual level, the Egyptian slavery was brought about by God (see Genesis ch.15). It taught us the importance of loving the stranger (Deuteronomy 10:19), it showed us the power of God when He redeemed us (Exodus 10:2) as well as His personal concern for us (Exodus 2:24); and it served as the "iron furnace" (Deuteronomy 4:20) which smelted us (the Israelites) into a nation and separated the dross.

See also: The Exodus

The later captivity:

The loss of the Ten Tribes (some 2650 years ago):

1) The spiritual reason was that for over two centuries the Ten Tribes had cut themselves off from the more-righteous tribe of Judah and the Temple, and had been more lax about the prohibition against idolatry. The prophets, such as Hosea, had warned them but were not heeded widely enough.

2) The temporal reason was that Assyria conquered them and exiled them.

See also:

Where are the Ten Tribes?

About the prophets

A positive result: Had the Ten Tribes not been exiled, the Tribe of Judah would have continued emulating their ways (Jeremiah 3:7-8) and might have gone lost like the Ten Tribes.

The First Destruction (some 2500 years ago):
1) The general spiritual reason was that God found the people of Judah to be below the spiritual level that was a requisite for having His presence among them. The prophets had warned them (Jeremiah 7:25) but were not sufficiently heeded (2 Chronicles 36:16). Once God's presence no longer felt welcome in the Holy Temple, its destruction was just a matter of time (Talmud, Rosh Hashanah 31a, and midrash Eichah Rabbah 1:43).
A more specific spiritual reason was the egregious sins of Menasheh, king of Judah (2 Kings 21:11-13 and 24:3).

2) The temporal circumstance was the fact that King Yehoiakim, after having been obedient to Nevuchadnezzar (king of Babylonia), became insubordinate (2 Kings 24:1); and Nevuchadnezzar responded by conquering the land of Judah, destroying the First Temple and exiling the populace.

Some positive results: the false prophets, at long last, were silenced forever. They had predicted that Judah would remain independent of Babylonia (Jeremiah ch.27) and no Destruction would take place.
Also, the lure of idolatry finally weakened, since the Destruction and Exile happened exactly as predicted by the true Prophets, who were the same ones who had spoken ceaselessly against dabbling in idolatry.

The Second Destruction (in 68 CE):
1) The spiritual reason was that the Jewish people were plagued by an internal enemy, the Sadducees, who had been dragging the spiritual level of the people downwards for many decades. These were men of power who (along the lines of the earlier Hellenizers) were less interested in Torah than in pleasure, politics, and obsequiousness to the Herodian kings and the Romans. Even the once-pious Hasmoneans had eventually become infiltrated by the Sadducees. They had fomented unnecessary wars, sown discord among the Jewish people (see Talmud, Yoma 9b), and had even killed a number of the leading Torah-sages (Talmud, Kidushin 66a).

2) The political trigger to the Second Destruction was the anti-Roman revolt fomented by the Zealots, who acted against the advice of the Rabbis and left the Romans no choice but to crush the people (Talmud, Gittin 56).

A positive result: The Second Destruction, as painful and tragic as it was, at least accomplished the disappearance of the impious cliques (as alluded in the parable in the Talmud, Gittin 56b, in which the "barrel of honey" represents Jerusalem and the Temple, and the "serpent" hints to the Zealots and Sadducees, among others). Once Jerusalem and the Temple were razed, the men of power melted away and the internal life of the Jewish communities returned to the aegis of the Torah-sages. (See: What did Rabbi Yochanan ben Zakkai do?)

Other non-traditional groups including the Samaritans and the Essenes also now permanently dissociated themselves from the Jewish people.

See also:

Jewish history timeline

The Diaspora

Answer 3

In the Old Testament, God allowed the Israelites to be captured or enslaved as a form of punishment for their disobedience and turning away from Him. This was often a consequence of their idolatry, disobedience to God's laws, and rejection of His guidance. It was meant to teach them a lesson, lead them to repentance, and ultimately bring about their redemption.