2 Kings - Chapter 14

We now read about Amaziah - King of Judah.

Now it happened, as soon as the kingdom was established in his hand, that he executed his servants who had murdered his father the king. But the children of the murderers he did not execute, according to what is written in the Book of the Law of Moses, in which the Lord commanded, saying, “Fathers shall not be put to death for their children, nor shall children be put to death for their fathers; but a person shall be put to death for his own sin.”

The quote is from Deuteronomy 24, and is saying first that people should not die for others' sins; but also that people should die for their own sin.

In Romans 6 Paul refers to this link between sin and death, but also shows how Jesus replaces death with eternal life:

"For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord."