Angels do not die like people
Jesus spoke of the life of people raised from the dead and said they would be like the angels in this respect: they cannot die any more (Luke 20:36). His main subject was resurrection, not a full description of angels, but the comparison gives a clear answer. Angels are not mortal creatures whose lives end as ours do.
Hebrews calls angels ministering spirits, sent by God to serve those who will inherit salvation (Hebrews 1:14). Scripture presents them as real created beings, not as human souls or imaginary forces. Yet their spiritual nature means we should not assume they are subject to bodily death.
Neither can they die any more: for they are equal unto the angels; and are the children of God, being the children of the resurrection.
The Bible does show spiritual conflict
Can angels be hurt? The Bible doesn't directly describe an angel being physically injured. So it would go beyond Scripture to give a confident picture of angels being wounded in battle.
Still, angels can be opposed. In Daniel's vision, a heavenly messenger says that the prince of Persia withstood him for twenty-one days, until Michael came to help (Daniel 10:13). This appears to describe conflict with an evil spiritual power connected with Persia, not merely an argument between people.
Revelation also describes war in heaven, with Michael and his angels fighting the dragon and his angels (Revelation 12:7-9). There is real resistance and defeat in that conflict. But the passage says nothing about angels bleeding, being maimed, or dying.
But the prince of the kingdom of Persia withstood me one and twenty days: but, lo, Michael, one of the chief princes, came to help me; and I remained there with the kings of Persia.
Fallen angels are accountable to God
The fact that an angel does not die does not mean an angel is beyond God's authority. Jesus speaks of everlasting fire prepared for the devil and his angels (Matthew 25:41). Their future is not independence or victory, but judgement.
Revelation says the devil will be tormented for ever and ever (Revelation 20:10). That is sobering language, though Christians have discussed details of the final judgement in different ways. The central point is plain: no spiritual being can resist God's justice forever.
Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:
God is greater than every angel
It is natural to wonder about powerful unseen beings. Scripture does not ask us to be fascinated by angels or frightened of them. Angels serve God, while Christ reigns over every authority and power (Colossians 2:15).
So the Bible's answer is modest but steady. Angels do not appear to die, and they can meet serious spiritual opposition, yet Scripture never records one being hurt or killed. Their strength is real, but it is never ultimate. God remains Lord over angels, evil powers, and every conflict we cannot see.