It is written:
“For if God did not spare the angels who sinned, but cast them down to hell and delivered them into chains of darkness, to be reserved for judgment;”. (2 Peter 2:4)
The New Testament teaches that the angels who sinned by committing sexual sin with human women were punished by being confined to the lowest section of Hades (i.e., Tartarus).
Jude really expounds upon this:
Jude 6-7-And the angels who did not keep their proper domain, but left their own abode, He has reserved in everlasting chains under darkness for the judgment of the great day; 7 as Sodom and Gomorrah, and the cities around them in a similar manner to these, having given themselves over to sexual immorality and gone after strange flesh, are set forth as an example, suffering the vengeance of eternal fire.
There is an important element of this passage in Jude which needs to be considered. Basically, Jude demonstrates that the sin of these angels was like the sin of the people of Sodom and Gomorrah: sexual sin!
“From the apostasy of Israel, Jude turns to the sin of the angels. He describes them as those who “kept not their first estate.” The word “estate” is the A.V. translation of archē. The word means first of all, “beginning.” Thus does the A.V. understand it. The angels left their first or original status as angels, their original position, to violate the laws of God which kept them separate from the human race, members of which latter race occupy a different category among the created intelligences than that of angels….The second meaning of archē is derived from the first, namely, “sovereignty, dominion, magistracy,” the beginning or first place of power. The word is translated “principalities” in Eph 6:12, and refers to demons there. Thus, this meaning of archē teaches that these angels left their original dignity and high positions. Archē is used, in the Book of Enoch (12:4) of the Watchers (Angels) who have abandoned the high heaven and the holy eternal place and defiled themselves with women (Mayor). This original state of high dignity which these angels possessed, Jude says, they did not keep. The verb is tēreō, “to guard.” The verb expresses the act of watchful care. That is, these angels did not fulfil their obligation of carefully guarding and maintaining their original position in which they were created, but transgressed those limits to invade territory which was foreign to them, namely, the human race. They left their own habitation. “Habitation” is oikētērion, “a dwelling-place,” here, heaven. “Their own” is idion, “one’s own private, personal, unique possession,” indicating here that heaven is the peculiar, private abode of the angels. Heaven was made for the angels, not for man. It is the temporary abode of the departed saints until the new heavens and new earth are brought into being, but man’s eternal dwelling-place will be on the perfect earth (Rev 21:1-3). “Left” is apoleipō. The simple verb leipō means “to leave.” The prefixed preposition apo makes the compound verb mean “to leave behind.” These angels left heaven behind. That is, they had abandoned heaven. They were done with it forever. The verb is aorist in tense which refers to a once-for-all act. This was apostasy with a vengeance. They had, so to speak, burnt their bridges behind them, and had descended to a new sphere, the earth, and into a foreign relationship, that with the human race, foreign, because the latter belongs to a different category of created intelligences than they. These angels are reserved in everlasting chains under darkness. “Reserved” is tēreō, and is in the perfect tense. That is, they have been placed under a complete and careful guard, with the result that they are in a state of being under this complete and careful guard continually. These angels are carefully guarded in everlasting chains. “Chains” is desmos, “a band or bond.” The word does not indicate that the angels are chained, but that they are in custody, detained in a certain place. The custody is everlasting. The Greek word is aidios, “everlasting.” “Darkness” is zophos, “darkness, blackness,” used of the darkness of the nether world…This verse begins with hōs, an adverb of comparison having the meanings of “in the same manner as, after the fashion of, as, just as.” Here it introduces a comparison showing a likeness between the angels of verse 6 and the cities of Sodom and Gomorrah of this verse. But the likeness between them lies deep-er than the fact that both were guilty of committing sin. It extends to the fact that both were guilty of the same identical sin. The punctuation of the A.V. is misleading, as an examination of Greek text discloses. The A.V. punctuation gives the reader the impression that Sodom and Gomorrah committed fornication and that the cities about them committed fornication in like manner to the two cities named. The phrase “in like manner” is according to the punctuation construed with the words “the cities about them.” A rule of Greek grammar comes into play here. The word “cities” is in the nominative case. The words “in like manner” are in the accusative case and are classified as an adverbial accusative by Dana and Mantey in their Manual Grammar of the Greek New Testament (pp. 91, 93). This latter construction is related syntactically, not with a word in the nominative case but with the verbal form in the sentence. All of which means that the words “in like manner” are related to the verbal forms, “giving themselves over to fornication” and “going after strange flesh.” In addition to all this, the Greek text has toutois, “to these.” Thus, the translation should read, “just as Sodom and Gomorrah and the cities about them, in like manner to these, having given themselves over to fornication and having gone after strange flesh.” The sense of the entire passage (vv. 6, 7) is that the cities of Sodom and Gomorrah and the cities about them, in like manner to these (the angels), have given themselves over to fornication and have gone after strange flesh. That means that the sin of the fallen angels was fornication. This sin on the part of the angels is described in the words, “going after strange flesh.” The word “strange” is heteros, “another of a different kind.” That is, these angels transgressed the limits of their own natures to invade a realm of created beings of a different nature. This invasion took the form of fornication, a cohabitation with beings of a different nature from theirs. This takes us back to Gen 6:1-4 where we have the account of the sons of God (here, fallen angels), cohabiting with women of the human race.” (Kenneth Wuest, Wuest’s Word Studies In The Greek New Testament, (E-Sword Edition, emphasis added-M.A.T.))
The Easy To Read Version makes this connection clear:
Jude 6-7-And remember the angels who lost their authority to rule. They left their proper home. So the Lord has kept them in darkness, bound with everlasting chains, to be judged on the great day. 7 Also, remember the cities of Sodom and Gomorrah and the other towns around them. Like those angels they were full of sexual sin and involved themselves in sexual relations that are wrong. And they suffer the punishment of eternal fire, an example for us to see.
What happened to the Nephilim offspring of these fallen angels?