Satan and his demons cannot die. They are spirit and were created as immortal beings (read Luke 20:36).
In Hebrews 2:14, the apostle Paul wrote that Christ would “destroy” Satan through His sacrifice. However, he was not saying that Christ would kill Satan. Webster’s Seventh New Collegiate Dictionary also defines destroy this way: “neutralize; to subject to a crushing defeat.” The word translated as destroy in this verse is the Greek word “katargeo,” which means “abolish, destroy, put away.” In I John 3:8, we read, “For this purpose the Son of God was manifested, that he might destroy the works of the devil.”
God will cast Satan into the lake of fire after the millenium (Rev. 20:10). This verse does not say that he will be there forever, but that his torment will last forever. The lake of fire will be quenched at the time of the establishment of the new heavens and the new earth (Rev. 21:1). But Satan and his demons will be punished throughout eternity.
The Bible only hints at the nature of the punishment of Satan and his demons. Jude 13 describes some of these demons as being “wandering stars [stars represent angels (Rev. 12:4)] to whom is reserved the blackness of darkness for ever.” Satan and his demons will be banished by God from the universe, to never again be able to influence anyone.