[Usual caveat applies: I am not a Greek scholar, so I draw on the knowledge of those who are]

The question to be explored here is whether the Greek word apollumi implies the complete and permanent destruction (annihilation) of something.

According to Bill Mounce, the basic meaning of this word is ‘to destroy, perish, lose.’

The following examples illustrate the range of meaning:

“to make void” (the wisdom of the wise, 1 Cor 1:19),

“to lose” (one’s reward, Mt 10:42),

“to be lost” (referring to the lost sheep of Israel, Mt 10:6).

In considering whether the word implies the complete and permanent destruction (annihilation) of something, Mounce urges us to pay attention to the context, as in:

““What have you to do with us, Jesus of Nazareth? Have you come to destroy us? I know who you are—the Holy One of God” (Mark 1:24).

“For if your brother is grieved by what you eat, you are no longer walking in love. By what you eat, do not destroy the one for whom Christ died” (14:15).

“The Pharisees went out and immediately held counsel with the Herodians against him, how to destroy him” (Mark 3:6).

“He will put those wretches to a miserable death and let out the vineyard to other tenants who will give him the fruits in their seasons” (Matt 21:41).

‘There is only one lawgiver and judge, he who is able to save and to destroy. But who are you to judge your neighbor?’ (4:12).

The disciples thought the storm would in fact kill them. They cry out to Jesus, “Save us, Lord; we are perishing” (Matt 8:25).

“And do not fear those who kill the body but cannot kill the soul. Rather fear him who can destroy both soul and body in hell” (Matt 10:28).

“Put your sword back into its place. For all who take the sword will perish by the sword.” (Mt 26:52)

“Or what woman, having ten silver coins, if she loses one coin, does not light a lamp and sweep the house and seek diligently until she finds it? (Lk 15:8)

(All ESV, emphasis added)

Of particular interest, from a theological point of view, are those passage which contrast destruction with eternal life, is in:

“For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.” (Jn 3:16)

See also:

‘They will suffer the punishment of eternal destruction, away from the presence of the Lord and from the glory of his might.’ (2 Thess 1:9)

Conclusion

Mounce concludes that while apollumi can mean ‘permanent and total destruction’ (annihilation), its semantic range is too wide to be sure if it carries this meaning in any particular case.  Attention to literary and theological contexts will give some assistance.