It's still going to go on for a while. There will be lots of them on Ebay and such even after they're not made anymore.
Ofcourse the actual point would be that sony should never have ripped out backwards compatibility from the PS3 so they could continue to sell two consoles at the same time, but they're not going to fix that anytime soon. And once the PS4 or whatever comes that -does- support PS2 games again (doubtful), none of those games are going to be relevant anymore. Let alone available for purchase from anywhere but Ebay or whatever people will be using.
But since Sony only profits from console sales and not from the games themselves, there really is no point for them to make PS2 games playable on newer consoles. No one is going to buy a PS4 just so they can play PS2 games. And i very much doubt having that backwards compatibility is going to be the deciding factor for a lot of people when it comes to purchasing one.
Game developers should simply re-release their PS2 games on the PS3. (Here's a clear and obvious hint for you SE). I'd love to play Xenosaga, i never got to play anything but the first one, which did get re-released, but the other ones i didnt play never did. Same for a bunch of obscure PS2 games that simply had its own charm and uniqueness.