"The door is not closed."

Translation: दरवाज़ा बंद नहीं है।

[PhilipSaxt]

Why doesn't "दरवाज़ा नहीं बंद।" work?

[soobee620]

Is है necessary here? Is it because बंद is not a verb?

[VZbLAexr]

I also have this question

[Gita-ji]

Yes.
बंद is an adjective.

[Danni473258]

I think there always has to be a verb in a hindi sentence. "closed" is not. It is an adjective. So hain is necessary even though there is nahi. Nahi is always placed before the verb. So nahi hain is correct at the end of the sentence.

[giuliet_]

So the fact is: when a verb is already present in a sentence the final "हूँ/है/हैं” is not necessary, but when there is not a verb in the sentence at the end we have to put "हूँ/है/हैं"

Did I get it right?

[Gita-ji]

Yes. You are right.
When नहीं is present, the final "हूँ/है/हैं” is not necessary if there is another verb in the sentence.