Mukavva koruyucu örtünün altında kaldı.

A helpful breakdown is:

• mukavva = cardboard
• koruyucu = protective
• örtünün = of the cover
• altında = under it / underneath it
• kaldı = stayed, remained, was left

So the structure is roughly:

• mukavva → the subject
• koruyucu örtünün altında → a location phrase, under the protective cover
• kaldı → the verb, placed at the end as is normal in Turkish

A very literal gloss would be:

Cardboard protective cover-of under-it remained.

Because Turkish commonly uses a genitive + relational noun pattern for things like under, on top of, inside, in front of.

So instead of using a separate preposition like English under, Turkish often says:

• X-in altında = under X
• X-in üstünde = on X / above X
• X-in içinde = inside X

Here:

• örtü = cover
• örtünün = of the cover

So koruyucu örtünün altında means under the protective cover.

The ending is -nün because:

• örtü ends in a vowel, so Turkish inserts a buffer n
• vowel harmony gives -ün

So: örtü + nün → örtünün

altında is made of several parts:

• alt = lower part, underside, below
• -ı = third-person possessive, roughly its
• -nda = locative, roughly in/on/at, with a buffer n

So:

• altı = its underside / its lower part
• altında = at its underside = under it

This is a very normal Turkish pattern.
So örtünün altında is literally something like at the cover’s underside, which English expresses simply as under the cover.

Because koruyucu örtü is an adjective + noun phrase:

• koruyucu = protective
• örtü = cover

In Turkish, when an adjective modifies a noun, the case ending goes on the noun, not the adjective.

So:

• koruyucu örtü = protective cover
• koruyucu örtünün = of the protective cover

This works just like:

• büyük ev = big house
• büyük evin = of the big house

The adjective büyük stays the same; only ev changes.
Same idea here with koruyucu and örtü.

It is the past tense of kalmak.

Depending on context, kalmak can mean:

• to stay
• to remain
• to be left
• to end up in a state or place

In this sentence, kaldı suggests that the cardboard remained or was left under the cover.

So English could translate it in a few natural ways:

• The cardboard remained under the protective cover.
• The cardboard stayed under the protective cover.
• The cardboard was left under the protective cover.

The exact best choice depends on the context.

It is the subject.

A native English speaker might wonder because Turkish word order is different, but here:

• mukavva is the thing doing the remaining/staying
• kalmak is an intransitive verb, so it does not take a direct object

So mukavva is not an object here.

If it were a definite direct object with a transitive verb, you would often see an accusative ending such as -yı / -i / -u / -ü. But here there is no such thing, because kalmak does not work that way.

Because Turkish normally places the verb last in a neutral sentence.

So the pattern here is:

• subject: mukavva
• location phrase: koruyucu örtünün altında
• verb: kaldı

This end position for the verb is one of the most basic sentence patterns in Turkish.

English often prefers:

• The cardboard stayed under the protective cover.

Turkish naturally prefers:

• Mukavva koruyucu örtünün altında kaldı.

Turkish does not have articles like English a and the.

So Turkish usually leaves definiteness to be understood from:

• context
• word order
• case marking
• possessive/genitive structures

Here, koruyucu örtünün altında naturally refers to the protective cover in context, even though there is no separate word meaning the.

So learners should not look for a direct equivalent of English the in every Turkish sentence.

Yes, but it would not mean exactly the same thing.

• koruyucu örtünün altında = under the protective cover / under that specific protective cover
• koruyucu örtü altında = under protective cover / under a protective cover / under cover in a more general sense

The version in your sentence sounds more specific because of the genitive + altında structure.

So if you mean a particular cover, örtünün altında is the more natural choice.

Here it functions as an adjective meaning protective.

It is related to the verb korumak = to protect.
So koruyucu literally has the sense of protecting or protective.

In other contexts, koruyucu can also be a noun, depending on usage, but in this sentence it is clearly describing örtü:

• koruyucu örtü = protective cover

So it works like an ordinary descriptive adjective here.