cave in vs fall in

cave in is a noun but fall in is not a noun.

Word	Noun	Adjective	Verb	Adverb
cave in	Yes	No	Yes	No
fall in	No	No	Yes	No

As verbs, cave in and fall in are synonyms defined as:

Other synonyms of cave in include break, collapse, founder, give, give way.

cave in (noun)	fall in (noun)
the sudden collapse of something into a hollow beneath it

cave in (verb)	fall in (verb)
break down, literally or metaphorically	break down, literally or metaphorically
	become part of; become a member of a group or organization
	to take one's place in a military formation or line