Nagare Kurosaki is Hisoka's father, and appears only later in the manga series, though never in the anime. Strict and traditional, he will seem to do anything to keep his family's secret under control. He appears ill to Watari and Tatsumi, but his poor physical condition is probably due to the swamp god Yatonokami possessing him. It is also noted that Hisoka gets much of his looks from his father, and they do, indeed, appear almost identical in hair and eye colour.
In both anime and manga whenever his son uses his powers he and his wife would lock him away, calling him a monster and refusing to call him their son. Though it's unclear if he felt remorse or sad after his son died for the way he treated him.