Unduly interested in death (6)
I believe the answer is:
morbid
(Other definitions for morbid that I've seen before include "Showing an unnatural interest in death and disease" , "Preoccupied with gloomy or unpleasant things" , "Of the mind, given to gloomy and unhealthy ideas" , "Diseased - gruesome" , "Inclined to dwell on unpleasant thoughts" .)