Under the entry for KATARGEW, BDAG has "to cause [something] to come to an end or to be no longer in existence, abolish, wipe out, set aside . . . TON TO KRATOS EXONTA TOU QANATOU destroy the one who has power over death Heb. 2:14" (page 525). This understanding of KATARGEW is consonant with Paul's words in Rom. 16:10 as well (note his use of SUNTRIYEI there and the part that Christians will play in the said "crushing" of the Devil).
[Jean] Why do you not mention the first meaning listed in BAGD for KATARGEW: "make ineffective, powerless, idle"? The fact that KATARGEW can mean "abolish" does not necessarily mean that Heb 2:14 automatically implies the destruction of the devil, although it may. According to LSJ the verb KATARGEW means "leave unemployed or idle." Other glosses includes: 1) make useless, cumber (the ground), 2) cause to be idle, hinder. LSJ also mentions as a second large category of meaning the idea to "make of no effect."
I did not mention the first definition because you had already alluded to it in your comments earlier. Secondly, BDAG lists Heb. 2:14 under the second definition (not the first one). While the significance attached to KATARGEW by BDAG is surely not definitive just because the lexicon construes KATARGEW in this manner, I think that BDAG's comments on KATARGEW in Heb. 2:14 certainly deserve consideration because we must not only ask what a word means: we must ask what a certain signifier denotes in a particular context. Based on other Scriptures that talk about the Devil, I believe that it makes more sense to group KATARGEW under the second definition found in BDAG (Gen. 3:15; Rom. 16:20).
LSJ is fine and its unequalled in the information that it provides. But we must keep in mind the priority that synchronic definitions have over diachronic ones. BDAG lists a number of Bible passages where KATARGEW seems to denote destruction or annihilation. This defintion seem apropos vis-a'-vis Heb. 2:14.