Yes, Sakae disappeared while trying to save Aoi. When she got infected with a parasite shrub, he used his power to suppress it. Doing so made his body disappear. His power kept the shrub inside Aoi at bay until she transferred some of that power to his baby boy. That transfer of power is probably why Sakae is able to take over Ashiya's body. Some of his soul/personality entered Ashiya along with the power. Anyway, Aoi used what was left of that power to help keep the shrub at bay for a few years (I think, going by how old Abeno was when she left). Sakae is probably dead, but hard to say at this point.

So basically his father, Sakae disappeared or got killed while saving Aoi??