hang by a hair vs hang by a thread

hang by a hair and hang by a thread both are verbs.

Word	Noun	Adjective	Verb	Adverb
hang by a hair	No	No	Yes	No
hang by a thread	No	No	Yes	No

As verbs, hang by a hair and hang by a thread are synonyms defined as:

hang by a hair and hang by a thread: depend on a small thing or be at risk

hang by a hair (verb)	hang by a thread (verb)
depend on a small thing or be at risk	depend on a small thing or be at risk