Employing the same terms that Paul used, one finds examples in earlier Jewish tradition of the suspension of persons on wood --- both dead and alive --- as a form of punishment and ultimate humiliation.
Of course the most important example here is the passage from Deuteronomy that Paul used as source material and is primary in Paul’s system ---
And if there be any sin with the judgment of death upon him, and he should die, and you should hang (κρεμάσητε) him upon a tree (wood, ξύλου) … by burial you shall entomb him that day, for being cursed by God is every one hanging (κρεμάμενος) upon a tree (wood, ξύλου); and in no way shall you defile the land which the Lord your God gives to you … (Deuteronomy 21:22-23)
In this passage, the generalized victim is killed before the suspension on wood. But the message is clear, anyone suspended on wood is “cursed by God”. To be cursed by God is the ultimate form of humiliation and punishment. And the body must be taken down and buried on that same day so the humiliation did not spread to all and “defile the land”.
And another example from the Jewish scriptures ---
Behold, even a tree (wood, ξύλον) prepared … and it was set straight up … Let him be staked/suspended/impaled (σταυρωθήτω) upon it! And Haman was hung (εκρεμάσθη) upon the tree (wood, ξύλου). (Esther 7:9-10, LXX)
The very same verb form (σταυρωθήτω) that Paul used is found in the Greek translation of this passage in Esther in the LXX. And like in Paul, the term is associated with hanging on a tree/wood. Whether Haman was suspended dead or alive in this passage in Esther is not entirely clear. However, when Josephus recounted those scriptural ‘events’ from Esther, he indicated that the suspension of Haman on the stake was an execution ---
“Haman … to be hanged on that stake (του σταυρού κρεμασθέντα) to be killed” (AJ 11.6.11, aka 11.267).
An important text found among the DSS materials provides the last example here ---
If a man is a slanderer and delivers his people to a foreign nation and does evil against his people, you shall suspend him on the wood/tree and he shall die. On the words of two witnesses and on the words of three witnesses he shall be put to death and they shall suspend him [on] the wood/tree [[...]]. If there is in a man a sin [worthy of the] death sentence and he has fled into the midst of the heathens and he has cursed his people and children of Israel, you shall suspend also him the wood/tree and he shall die, and you shall not let a corpse remain on the wood/tree overnight, you shall indeed bury him by day, for a [man] suspended on wood/tree is cursed by God and men, thus you shall not defile the land which I am giving to you [as] inheritance. (Temple Scroll, Col. 64)
In the second sentence, a post-mortem suspension seems to be implied, but at least one other translation is less clear. However, the text clearly describes in two places the suspension of a live victim for treasonous acts. The prohibition of leaving the corpse overnight as found in Deuteronomy is repeated here in this text.
In the wide realm of Jewish tradition whether the victim was executed first or suspended alive may have been determined by the specific crime committed, may have varied over time, and may have been at the discretion of those in power and imposing the punishment.
I think the important take-away is that within the wide realm of Jewish tradition in Paul’s day, some vanquished foes and certain law-breakers were publicly suspended on wood --- whether dead or alive --- in order to impose the maximum humiliation.
robert j