The κατάθεμα of verse 5
Didache XVI:5 ends with “but they who endure in their faith shall be saved by the curse (κατάθεμα -katathema) itself”, and this saving, comforting action is associated with the fiery trial with its many casualties and with many others who get in big trouble.
The meaning of κατάθεμα is obscure, and so this phrase has been commented upon extensively. Some scholars believe it refers to the fiery trial, but most of them believe that κατάθεμα describes Jesus.
In Apostolic Fathers I (Loeb Classical Library 24) Kirsopp Lake comments his translation as follows: “The meaning is obscure; but there seem to be other traces in early literature of a doctrine that each curse also contained the elements of a counterbalancing power to salvation.”
In The Didache in Context Nancy Pardee devotes a whole chapter to κατάθεμα and after her linguistic explorations she suggest that its meaning might be ‘utterly condemned’, and she explains that ‘the semantic range of κατάθεμα seems to favor the interpretation that the faithful will be saved by Christ themselves’.
In La Didachè – Instructions des Apôtres Jean-Paul Audet derives κατάθεμα from κατατίθημι and through κατάθεσις (katathesis - deposition) he continues to ‘the deposited corpse’ and finally ends at ‘tomb’. So here as well the Jesus of the gospels is involved.
This saving, comforting, supporting action of Jesus took place during the war. There is no trace that his act of salvation during the war was founded on events that would had taken place decades before.