It is true. Hebrews says Angels are ministering spirits. Jesus said angels cannot die so they will stay in the lake of fire forever.
Jesus was speaking of heavenly angels not fallen angels. Fallen angels can and will die and be consumed by eternal fire and they will never exist again.
Even the devil will be destroyed so his fallen angels will also.
Heb_2:14 Forasmuch then as the children are partakers of flesh and blood, he also himself likewise took part of the same; that through death he
might destroy him that had the power of death, that is,
the devil ;
Even the devil will be destroyed.
Eze 28:18 Thou hast defiled thy sanctuaries by the multitude of thine iniquities, by the iniquity of thy traffick; therefore will I bring forth a fire from the midst of thee,
it shall devour thee, and I will bring thee to ashes upon the earth in the sight of all them that behold thee.
Eze 28:19 All they that know thee among the people shall be astonished at thee: thou shalt be a terror, and
never shalt thou be any more.
He will be devoured by fire, turned to ashes and shall never exist anymore. That's Annihilation.