He was one of the unfortunate ones to witness the death of Future Goku in Age 766. In Age 767, the Androids killed Z Fighters with the exception of Future Gohan and Future Trunks. Future Puar now lives on board a submarine near Kame House with Future Oolong, Future Master Roshi, and Future Turtle.
It is unknown whether he survived when Goku Black invaded Earth. Since it has been stated by Future Trunks that there's hardly any humans left alive in his timeline.