"the angels that sinned...the angels
that kept not their first estate"
2nd Peter 2v4 & Jude 6
Note the identity of language in these two quotations - "God...delivered them into chains of darkness, to be reserved unto judgment"…"he hath reserved in everlasting chains under darkness unto the judgment of the great day".
These "angels" refer to those recorded in Numbers 16 who mounted a rebellion in Israel. Their leaders, Korah, Dathan, and Abiram rebelled against Moses and therefore against God - for which sin they were destroyed. "They, and all that appertained to them, went down alive into the pit, and the earth closed upon them: and they perished from among the congregation"-v33, see v31,32 & below.
The points of clear identification are these:
Their appointed position was to "minister" to the assembly - Numbers 16v9 - and they were thus fitly described as "angels" from the Greek 'aggeloi'. Strong's Concordance defines 'aggelos' as "a messenger; esp. an "angel"; by impl. a pastor"...and the root word of 'aggelos' is 'ago' - "to lead". See also Revelation 2 & 3 - the "angel" of each "ecclesia" comprised those who were appointed to minister to the assemblies, and to lead them in Divine worship.
Their "first estate" or "principality" (Jude 6 mg.) was that of "princes" (RSV "leaders") - Numbers 16v2.
They "kept not their principality, but left their own habitation" when they sought the priesthood and rebelled - Numbers 16v1-15.
The "angels that sinned" were "sinners against their own souls" - Numbers 16v10, 38.
They were "delivered into chains of darkness" when they were swallowed alive by the earth - Numbers 16v31-33. The Greek word 'tartarus' is translated as "hell" in 2nd Peter 2v4. It has the meaning of the lowest place in the earth, and thus a better description of their end could not be imagined.
The "judgment of the great day" quite obviously refers to the Judgment Seat of Christ - cp Acts 2v20;10v42;17v31; 2nd Timothy 4v1 etc. This identifies these events with the Adamic creation. And they cannot refer to immortal angels.
It is impossible for immortal angels and those who will be granted immortality and become "equal unto the angels" (Luke 20v36) to sin again. Their nature will have been changed to that which Christ now possesses, though when He "was made to be sin" (2nd Corinthians 5v21), it was like ours, i.e. "sinful flesh" (Romans 8v3).
He is now "without sin" (Hebrews 9v28), and accepted believers "shall be like him" (1st John 3v2) and will therefore also be "without sin" - being "delivered from the bondage of corruption into the glorious liberty of the children of God" (Romans 8v21) "neither can they die any more" (Luke 20v36) - which quotations eliminate the possibility of sin.
At the change to divine nature, "the law of sin and death" (Romans 7v23,25 & 8v2) will be no more. Jesus taught Nicodemus "That which is born of the flesh is flesh; and that which is born of the spirit is spirit" (John 3v6). In such a glorified state there will be complete harmony forever with the Father. This is the hope of the believer, founded upon the infallible word of God, "as an anchor of the soul, both sure and stedfast" (Hebrews 6v19).
concerning the word 'sin'
link to 'sacrifice' - page 2.
The examples in 2nd Peter and Jude from the history of Israel and earlier in the Adamic creation, of which they had the records, were chosen because of their notoriety, thus ensuring that the lessons would be clearly discerned. Note 2nd Peter 1v12 - "Wherefore I will not be negligent to put you always in remembrance of these things, though ye know them" - & Jude 5 - "I will therefore put you in remembrance, though ye once knew this…". Also see Numbers 26v9-11 concerning the sinners' notoriety & unforgettable end.
Paul also chooses the case of Korah and company in 2nd Timothy 2 to illustrate the sin of rebellion and how it should be dealt with. This OT rebellion was an extreme case, so much so that "the censers of these sinners" were commanded to be made into "broad plates for a covering of the altar".
They were to be "a sign unto the children of Israel". The censers were made of brass, and were taken "out of the burning", thus illustrating that sin's flesh must be purified in the fire of affliction - Numbers 16v39,38,37.
This purification by sacrifice (to become "fine" or "burnished" or "polished" brass) is an attribute of the glorified multitudinous Christ-body, cp. Revelation 1v15; Ezekiel 1v4, 7, 13, 27; Daniel 10v6. The Christ-head of this body has been purified by His own sacrifice, cp. Hebrews 9v23-26. Without such sacrifice, salvation for both Himself and His people would have been impossible.