Future Dr. Brief's life was exactly the same as his main timeline counterpart's until August of Age 764 when Future Goku used the Instant Transmission to arrive on Earth and kill Future Frieza and Future King Cold.
Dragon Ball Z
The History of Trunks
Main article: Dragon Ball Z: The History of Trunks It is revealed by Future Bulma that he had passed away sometime before Age 780. However, it is unknown what his cause of death was; he could have been killed when the Androids destroyed West City or died from natural causes.
Main article: Trunks Saga Future Trunks briefly alludes to Future Dr. Brief when privately thanking his grandfather for his watch while locating the point where Goku would land and guiding the Dragon Team to it.
Dragon Ball Super
"Future" Trunks Saga