Well. It's complicated. The short version is this, and here's a full video. Multiple people are working on the preservation of flash games.
Sites like Newgrounds are making their own launchers, there are projects which collect thousands, and I mean thousands of games. You know how some older games on AG are extremely slow and laggy? That's because of changes in Flash. Those projects will help those games become playable again.
Some developers also change their games to fit in. That includes the NinjaKiwi and the Henry Stickmin collections.
Now, as for Armor Games? We don't know. I think that AG will move on from Flash games to become a pure indie publisher. It seems to have been moving towards that for a while now. HTML5 games will most likely continue being hosted, though. (Flash game) Quests? No idea. I doubt AG will be able to spare the developers to think of a solution, either. Also worth mentioning that people have moved away from web games. AG has just 3-4% of the popularity it had at its peak in February of 2011. I doubt they consider that it's "worth it" now, too...
Did you know AG is the most popular in Idaho? I'm saying that because I've somehow psychologically programmed myself to identify with Idaho at every turn.
There was a time HTML5 quests were considered being added, but no new quests have been added in a while now.