It is unknown if he, along with the other lower Kais, was hunted down by Goku Black and Future Zamasu as part of their Zero Mortals Plan as, due to being weaker than the Supreme Kais, he would be unlikely to pose a threat to their goals.
Video game stories
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 Z Fighters, 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.