Thankfully, there isn’t the slightest chance of such a scenario coming to pass in my lifetime, so I’m not losing any sleep over it.
The Bible does not provide capital punishment for all sins. Many crimes like theft require restitution. Perjury requires the punishment which the innocent charged person would have suffered. (That's equitable.) The Bible does provide for stringent standards of due process -- capital crimes require 2 or 3 witnesses -- not a single witnesses, not merely circumstantial evidence. If you are truly interested, you are free to discover these things yourself by reading Exodus, Leviticus, Numbers and Deuteronomy (and Hebrews).
However, the sins we have committed do condemn us to God's just punishment in the after life. All have sinned and come short of the glory of God. He makes the rules, but he has also provided an escape.
16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. 17 For God sent not his Son into the world to condemn the world; but that the world through him might be saved. 18 He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God. 19 And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil.
(Gospel of John, Chapter 3 verses 16 thru 19)