in the last chapter did the black head died

Yea. The plane he took to get to wherever Izumi was crashed, so that's why he said it was okay for him to be there, but the whole thing was a 'dream' that no one else could see. Kinda confusing, but I guess that's what happened.

they both died in the end right?

Yup. They both died and they were able to be together in the afterlife. Takaaki came for Izumi.