fall by the wayside vs drop out

fall by the wayside and drop out both are verbs.

Word	Noun	Adjective	Verb	Adverb
fall by the wayside	No	No	Yes	No
drop out	No	No	Yes	No

As verbs, fall by the wayside and drop out are synonyms defined as:

fall by the wayside and drop out: give up in the face of defeat of lacking hope; admit defeat

Other synonyms of fall by the wayside include chuck up the sponge, drop by the wayside, give up, quit, throw in, throw in the towel.

fall by the wayside (verb)	drop out (verb)
give up in the face of defeat of lacking hope; admit defeat	give up in the face of defeat of lacking hope; admit defeat
	leave school or an educational program prematurely
	withdraw from established society, especially because of disillusion with conventional values