The following sentence was in an N4 review test:
私の本棚には 買ったまま 読んでいない まんが が たくさん あります。
The meaning, as I grasp it, is "There are a lot of books that I bought in my bookshelf that are left unread."
But this is confusing because the grammar pattern, Past (た) + まま essentially means "(while, left, stay) + verb" as in:
妹は制服を着たままで寝てしまいました。
My younger sister fell asleep while wearing her school uniform.
How does 買ったまま make sense in this context?
The link you have given defines 〜たまま as "remains unchanged". Before examining your examples lets take an ordinary example:
弟はテレビをつけたまま寝てしまいました。
A natural translation would be:
My younger brother fell asleep in front of the television.
A more literal translation, employing the idea of "remains unchanged" would be:
"My younger brother fell asleep while the TV was still on."
Please note that while these two sentences are different in English, they amount to the same thing. But, we had to employ a certain amount of "literary license" to get to what I think you would agree is the more natural English equivalent.
In both your examples your reference has given you the more natural translation. It sounds like you are looking for the "in-between" sentence that gets us from the Japanese to the natural English sentence using the explanation on your link of "remains unchanged". I would suggest:
私の本棚には 買ったまま 読んでいない まんが が たくさん あります
There are many comics (ie manga) on my bookshelf that are unread, just as they were when they were bought. (ie new, in mint condition...remain unchanged from when they were first bought)
In the second sentence:
妹は制服を着たままで寝てしまいました。
My younger sister fell fast asleep [unchanged] still wearing her uniform.
We can conveniently use the expression "remains unchanged" here to convey the message that she did not change out of her day clothes (uniform) to her night clothes but this would be to miss the point that translating Japanese requires us to take the unwritten context into account. The situation that remained unchanged was that she did not take off her uniform. This type of expression is often (but not always) used to convey that an action that would normally be done before a second action did not take place.
A more plain use for まま would be:
窓は開けたままだった｜The window had been left open.
話を聞いたまま話す｜tell a story just as one heard it
Look a little closer at the link you posted. It explains this grammar structure as meaning "the situation A remains unchanged." This can have the meaning of "while" in English, but that's not necessarily a good way to think of it. In your example "妹は制服を着たままで寝てしまいました。" it is approximated in English as "while" because that's how we might say it in this case. But try to think of it in the "remaining unchanged" meaning. The younger sister fell asleep, and her uniform was left on. The suggestion is that she would have normally changed into something else before falling asleep.
The point is you need to think of it as a continuation of an old state and especially unchanged when you might expect a change. So when we apply this to the sentence you're confused about, it might be a little clearer. On your bookshelf are many books that are as they were when you bought them, as in still new, unopened and unread. This is a little more abstract than something physical like wearing a uniform to bed or wearing something while it's still wet or what have you, but it works.
Just try your best to avoid linking words, phrases, and other constructions directly to English words/phrases and instead try to internalize the deeper meaning.
The 着る example might be confusing you, since 着る and "wear" do not match each other very well with respect to aspect. Aspect-wise 着る matches "don" better (着る is a change-of-state verb).
So an unidiomatic, but true-to-aspects translation of the 着る example might be:
My sister fell asleep with her clothes donned
and likewise, your 買う example might be translated
... many unread books that are like newly-bought
The "while" translation is misleading and only works in the 着る case because 着る is a change-of-state verb, while "wear" describes a state.
