I suggest sort of archiving the site: leave the hacks and the forums (for ulterior use, reference, nostalgic value, and especially for still updating games), scrub everything else (if not removing stuff, making them non-responsive). It would take a load off servers, and the site would still exist and function for those who want to use it. I wouldn't mind it if it went over to a free hosting service, if costs can't be covered, the one thing I would mind is if it ceased to exist/function. I don't care about emotes, lottery, profile beautification, etc, but I do care about the hacks. If that part stays, I say the rest can go. Regarding the trainer... I don't see a need to do anything with it. It works, doesn't it? Then let it keep on working, there is no real need to fiddle around with it. Well, maybe remove the login, so if the site dies it can still be used? :p This site has been a tremendous support for me, for almost a decade, both with cheats and hacks, both with learning, and I'd hate to see it die. But with kongregate shutting its doors, I can see the same fate befalling konghack too.
A side idea, not sure if it's even feasible, but still, better to put it out in the open: is there a possibility to make all game cheats/forums migrate to the wemod forums? It would add a useful aspect to their forums, and save the cheats here for the future.