Dragon Ball Super
In the Future Trunks Saga, Future Trunks mentions that Future Korin is no more - highly implying that he has died. This prevents Future Trunks and Future Mai from having Senzu beans to tend to their wounds. However it is unknown how he died, either during the Androids attack or Black's invasion.
Video game stories
Shin Budokai Another Road
Future Korin survived the attack of the Androids. However, years later, Korin Tower is attacked by Future Babidi's Fighting Puppets and Future Korin has to get away. Future Korin meets Future Trunks while the latter is on his way to West City to retrieve his Time Machine, and Future Korin gives him some Senzu Beans.