living dead vs dead soul

living dead and dead soul both are nouns.

Word	Noun	Adjective	Verb	Adverb
living dead	Yes	No	No	No
dead soul	Yes	No	No	No

As nouns, dead soul is a hypernym of living dead; that is, dead soul is a word with a broader meaning than living dead:

living dead: a dead body that has been brought back to life by a supernatural force
dead soul: someone who is no longer alive

Other hypernyms of living dead include dead person, deceased, deceased person, decedent, departed.

living dead (noun)	dead soul (noun)
a dead body that has been brought back to life by a supernatural force	someone who is no longer alive