Regarding Mary, the angel told Joseph; "She will give birth to a son, and you are to name him Jesus, for he will save his people from their sins.” (Matthew 1:21) Since sin leads to death, Jesus was to save those exercising faith from both sin and death. (Romans 6:23)
I believe we will also be saved from pain, sorrow, sickness, and from evil, wicked people. (Revelation 21:3,4, Psalm 37:10,11)
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It is certainly true that all pain, sorrow, sickness , and other suffering is caused by being born from sinful parents, thereby, inherited death.
Jesus was the Redeemer sent forth by God, offering up his perfect, sinless human life
(that could have remained forever, as he was not born of Adam, and therefore, with God as His Father, was 'without sin', and was not under the death penalty of sin)
once for all time.
He paid the Ransom price for sin to The Lifegiver and Creator, Jehovah God,
for all mankind who would put faith in the ransom sacrifice , believe in Him as the One sent forth by God, and obey his commandments.
Helping others by warning them of the alternative, and teaching those willing to learn, insures the promise of extended life thru the resurrection hope.
Ezekiel 33:9
But if you warn someone wicked to turn back from his way and he refuses to change his course, he will die for his error, but you will certainly save your own life.
So, what obedient ones are 'saved from' is the ETERNAL death sentence. As long as there is life, there is hope. Once a life is extinguished, it is up to God to resurrect the dead ones, giving them a possible second chance to life.
Eccl. 12:13.
So your post is basically correct according to what the Bible really teaches.