Near to death (2,8)
(Other definitions for dying that I've seen before include "On one's last legs" , "Declining" , "Perishing" , "Ceasing to function" , "On the point of death" .)
(Other definitions for in extremis that I've seen before include "at a desperate point" , "as last resort" , "dying" , "Facing death" , "At the point of death" .)