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There's a very popular game series called Middle-earth: Shadow of Mordor. This series has very interesting mechanic called Nemesis system. From wikipedia:
The game can track any Uruk that the player comes into contact with. While there are "generic" Uruk for the player to fight en masse, and will be as cannon fodder as part of Sauron's armies, the game will begin tracking Uruk that perform any notable talents within the game, such as killing the player, or surviving an encounter with the player. These Uruk will be promoted into captains. Alternatively, being killed by a leader will cause the current mission to be cancelled and the player returned to a safe point to continue exploring, and the leader will gain additional power, making him more difficult to defeat in the next encounter. If the procedurally generated Orcs survive an encounter with Talion, they will also be promoted. Further, such deaths are tracked through online servers, and the player's friends on the various network services will be notified of this death and be offered the chance to accept a Vendetta mission, and exact revenge on the Uruk. If the mission is successful the game will give rewards to both the original player and the victorious friend. Uruks that survive their encounter with Talion will remember this when Talion combats them again; for example, an Uruk who was thrown into a fire by Talion might want revenge on him for being disfigured.
I think, this could be implemented to the mainline series. Sure, Pokemon games already have something similar (rivals, trainers that can be rematched) but not in that kind of scale. I imagine, that when our character defeat some random trainer, he/she has a chance to comeback and become our new rival. Even better would be, if his/her Pokemon team will be counter for player team that defeated him/her in the last time.