run-down vs derelict

run-down is not a noun while derelict is a noun.

Word	Noun	Adjective	Verb	Adverb
run-down	No	Yes	No	No
derelict	Yes	Yes	No	No

As adjectives, run-down and derelict are synonyms defined as:

Other synonyms of run-down include creaky, decrepit, flea-bitten, woebegone.

run-down (noun)	derelict (noun)
	a ship abandoned on the high seas
	a person without a home, job, or property

run-down (adjective)	derelict (adjective)
having the spring unwound	in deplorable condition
worn and broken down by hard use	failing in what duty requires
	forsaken by owner or inhabitants
	worn and broken down by hard use