Pardee, Nancy. "The Curse that Saves (Didache 16.5)." in Jefford, Clayton (editor). The Didache in Context: essays on its text, history, and transmission. Leiden: Brill, 1995, 156-176.
Pardee considers the word κατάθεμα as used in Didache 16.5 to be worthy of special study as it may provide insight into eschatology, soteriology, and Christology all at once (Pardee 1995, 156). She notes an irony by which a curse rescues from a curse, and observes that fire was typically used to destroy items considered accursed (Pardee 1995, 157). Pardee notes the study of the term cannot possibly confirm the identity of the curse, but that it can refine our understanding of possible referents (Pardee 1995, 158).
Pardee notes that the word group ἀνάθημα / ἀνάθεμα is commonly used, and refers in Thucydides and after for something set up, such as a person or thing designated for special service (Pardee 1995, 159). In Jewish and Christian usage it is specifically something which can serve as a negative example, so something accursed. Pardee reviews usage of ἀνάθημα as it appears in the Dead Sea Scrolls, since they are closer in time to the Didache than is the ancient Greek literature (Pardee 1995, 163)./ Pardee provides a number of passages and brief comments.
Pardee concludes that the ἀνάθεμα word group is not used in a negative sense earlier than the Septuagint. Usint it that way
outside of Judeo-Christian literature is rare and late" (Pardee 1995, 168). The word used in Didache 16.5, κατάθεμα, appears more rarely, and never has positive connotations (Pardee 1995, 169). In the end, Pardee concludes that the word is used clearly for a curse, and that this "curse itself" is most likely a veiled reference to Christ.