"Future" Trunks Saga
During the Future Trunks Saga, it is revealed that he and the remaining gods (save for Future Shin and Future Beerus who had died during the future timeline's Magic Buu conflict and Future Zeno) were killed by Goku Black and Future King Kai's former Universe 10 counterpart Future Zamasu the former North Kai of Universe 10.
Other Dragon Ball Stories
Shin Budokai - Another Road
When Future Trunks is about to fight against Future Dabura, Future King Kai uses telepathy to talk with Future Trunks and advises him to protect the cities. Future King Kai contacts Future Trunks again when Future Korin gives some Senzu Beans to Future Trunks, and he teaches Future Trunks how to use the beans. When Future Trunks comes back with the Dragon Team, Future King Kai teaches him to fight in team. Future King Kai uses telepathy again when Future Trunks is on New Namek in order to teach him how to use the Dragon Radar.