Since the PS3 era, every PlayStation system was released with a trophy system. Platinum hunters became a thing and every now and then we find some ridiculous task behind a simple bronze trophy. On the other hand, the lack of support for PSX and PS2 titles was always lamented among players.
However, that last situation might actually change. On a subreddit thread, an user found out that there was a patent published on March 18, which is described as "Method and apparatus for awarding trophies." In short, players would be able to earn trophies in "previously released or sold video games, without modifying the original game."
There's still no official announcement from Sony. Nonetheless, you can read more about the patent here.