The hierarchy of horror was loss of life, loss of possessions, loss of burial, that is, destruction of body, destruction of family, destruction of identity. For the ancient world, the final penalty was to lie unburied as food for carrion birds and beasts. After Octavius, later emperor Augustus, had defeated Julius Caesar's murderers at Philippi in October of 42 B.C.E.,
He did not use his victory with moderation, but after sending Brutus' head to Rome, to be cast at the feet of Caesar's statute, he vented his spleen upon the most distinguished of his captives, not even sparing them insulting language. For instance, to one man who begged humbly for burial, he is said to have replied: "The [carrion] birds will soon settle that question." (Suetonius, The Deified Augustus 13.1-2)
As with Brutus' companions for Augustus, so with Sejanus's companions for Tiberius. Between 26 and 31 the emperor Tiberius ruled Rome from the island of Capri off Naples, and Sejanus, prefect of the praetorian or imperial bodyguard, plotted against him in Rome itself. But in October of 31 C.E. Tiberius moved swiftly against him, and many of his fellow plotters chose immediate suicide:
For these modes of dying were rendered popular by fear of the executioner and by the fact that a man legally condemned forfeited his estate and was debarred from burial; while he who passed sentence upon himself had his celerity so far rewarded that his body was interred and his will respected. (Tacitus, Annals 6.29)
Lack of proper burial was not just ultimate insult, it was ultimate annihilation in the ancient Roman world. There would be no place where the dead one could be mourned, visited, or remembered. Think of all those Roman graves whose epitaphs address the passerby in direct discourse: the I can still speak to you.
It was precisely that lack of burial that consummated the three supreme penalties of being burned alive, cast to the beasts in the amphitheater, or crucified. They all involved inhuman cruelty, public dishonor, and impossible burial. In the first two cases, that's obvious: there would be hardly anything left for burial. In the case of crucifixion, it presumes that the body was left on the cross until birds and beasts of prey had destroyed it. Indeed, in Roman texts two items occur again and again in connection with crucifixion. First, the crucified one is especially a disobedient slave or anyone considered an equivalent nobody, hence its designation as the slave penalty. Second, the crucified one is left unburied on the cross as carrion. Those twin concepts come together in an imagined interchange between Horace and one of his slaves published in 20 B.C.E.
If a slave were to say to me, "I never stole nor ran away": my reply would be, "you have your reward; you are not flogged." [If a slave were to say to me,] "I never killed anyone":[my reply would be,] "You'll hang on no cross to feed crows." (Epistles I.16:46-48)
Crucifieds were left, kept, or guarded on the cross even after death if there was any chance that relatives or friends might take them down for proper burial before it was absolutely too late. Such an act would be, of course, extremely dangerous unless done with bribes or permissions.
I have know cases when on the eve of a holiday of this kind [imperial birthdays], people who have been crucified have been taken down and their bodies delivered to their kinsfolk, because it was thought well to give them burial and allow them the ordinary rites. For it was meet that the dead also should have the advantage of some kind treatment upon the birthday of the emperor and also that the sanctity of the festival should be maintained. But Flaccus gave no orders to take down those who had died on the cross. (Against Flaccus 83)
Burial of crucifieds by their families is certainly possible. In fact, we now have both material as well as textual evidence for their possibility.
...However it was managed, be it through bribery, mercy, or indifference, a crucified person could receive honorable burial in the family tomb in the early or middle first-century Jewish homeland. Second, with all those thousands of people crucified around Jerusalem in the first century alone, we have so far found only a single crucified skeleton, and that, of course, preserved in an ossuary. Was burial, then, the exception rather than the rule, the extraordinary rather than the ordinary case?
* Deuteronomy 21:22-23
If a person commits a sin punishable by death and is executed, and is then hung on a tree, his body must not remain all night on the tree; instead you must bury him that same day, for the one who is hung on a tree is cursed by God.