In my textbook I found this sentence:
If 面熟 is an adjective, why is it used after 人 (to indicate a "familiar-looking person")?
Can 一个人面熟 be rewritten to 一个面熟人 without modifying the sentence's original meaning?
This is a classic example of a topic-comment construction that is prevalent in Chinese. In this case, 面熟 is not serving as an adjective to the noun, but rather as a comment on the topic.
All adjectives in Chinese can function as verbs (Chinese adjectives are sometimes called stative verbs for this reason); as such, they can function as a predicate by themselves. Because Chinese is a pro-drop language, predicates can serve as their own clauses in a comment.
To answer your second question, you can't put 面熟 before the noun in this case without restructuring the sentence. 却 is used to connect two clauses together. If you make 面熟 into an adjective, it's no longer a clause, so the usage of 却 will no longer make sense.
In my opinion, here “面熟" is the complement to the clause "常常看着一个人". That's why it is used after "一个人" though it's really an adjectvie. In English, you would see similiar consctructions:
He makes me angry.
I found her so beautiful.
He is coming here with the final decision in his mind.
I saw a man apparently faimilar to me yesterday, but I could't recall who he is.
For your second question, you could put "面熟“ before "一个人" to modify it, but generally we use "面熟的", or it sounds strange. You could say,
A little reminder:
In Chinese, the elements of sentences include:主语(Subject),谓语(Predicate),宾语(Object),定语(Attributive), 状语(Adverbial) and 补语(Complement). You may want to understand what they are and how to use them first, before you could analyze the sentence structures.
If you look at 面熟 and it's meaning 面 = appeared / appearance 熟 = familiar
The sentence in English reads more like this: "I saw a person who appeared familiar (to me)"
In Chinese this seems a bit strange, but this is a common construct. See this example:
Maybe this reads better with a comma:
Which you will notice if you search Google for "一个人面熟" there are quite a few examples of:
... 一个人, 面熟
You can also put the characters in front but you need to use the possessive 的 as in:
Which a good counter example in English to the sentence I provided above is more like:
"I saw a very familiar looking person"