grammar - 接続 of compound words ending with verb-ず

Question

In my understanding, the part of speech of a compound word is determined by its ultimate morpheme. (複合語の品詞は、後にくる語（形態素）の品詞によって定まります)

蒸す(V)＋暑い(Adj) → 蒸し暑い(Adj)

持つ(V)＋物(N)　　→ 持ち物(N)

and a verb in its -ず form can be roughly treated as an adverb.

食事をたいらげた　　　　 ate up a meal

食事を残らずたいらげた 　ate up a meal completely (without any bit of remain)

Here comes the question. I find compound words ending with verb-ず have a variety of 接続, none of them are used as an adverb, e.g.

知らずしらずのうちに　(resembles noun＋の＋うち)

役立たずな人　(resembles 形容動詞＋な＋人)

恥知らず者　　　(resembles イ形容詞＋者)

How should I understand such a variety of 接続? and when to use which 接続?

p.s.

1. I saw the subtitle "役立たず共め" in an anime, saw there is an example sentence "恥知らずなことをする" in my dictionary, and therefore I came up this question.
2. I found compound words ending with verb-ず pretty versatile; it can be an adverb (in 日本人を恥知らず呼ばわりする外国人を批判する), a na-adjective (in 恥知らずな噓をつく), or a noun I guess? (in 馬鹿で恥知らずの人間になる) These three sentences are found on the Internet.

Answer 1

If you already know the masu-stem of some verbs can act as a noun or na-/no-adjective, you can think these ず-words are almost the same except that negation is included as part of the word. That is to say, there are a few lexicalized ず-words that work as nouns or na-/no-adjectives. Just like non-negative ones, many ず-words have unpredictable meanings, and you have to learn them individually. 役立たず and 恥知らず are typical examples, and they can safely work as nouns, na-adjectives and no-adjectives.

Other examples:

• 向こう見ず reckless
• 親知らず wisdom tooth​
• 医者要らず keeping doctor away
• 水入らず en famille; private
• 鳴かず飛ばず obscure; inactive; unsuccessful
• 飲まず食わず without eating and drinking
• 開かず (as in 開かずの間 locked/sealed room)
• 寝ず (as in 寝ずの番 night watch)

This type of ず is integrated in a fossilized expression, and you cannot arbitrarily add or remove it. For example, 恥知り and 向こう見 mean nothing. (Well, 飲み食い happens to mean something a bit different...) New words are very rarely coined using this grammar, but おにぎらず is a fairly new buzzword made from おにぎり.