- a) I threw away the worn-out socks.
b) I put the socks worn out on the table. [INCORRECT]
c) These socks are worn out.
d) Something worn out deserve to be thrown away.
Before writing my answer about "worn out", let me tell something about the sentence 1.b) and 1.d). Sentence 1.b) is not a correct sentence, whereas sentence 1.d) is correct.
A pronoun like something can be post-modified by an Adjective Phrase (AdjP), here worn out. But in sentence 1.b) the noun - socks - can not be post modified like this way. [For further reference turn to page no. 1293 sec 17.56 of Quirk et al.]
So for discussion, I will exclude the incorrect sentence 1.b).
In all the sentences above, "worn out' is adjectival, and not verbal.
We will examine them one by one -
I threw away the worn-out socks.
Here we need to concentrate on the Noun Phrase (NP) - the worn-out socks. The bold part in that phrase is a modifier of the noun - socks. But what word class it is in?
Generally speaking, it is best to test such cases to alter its position. Let's alter its position:
I threw away the socks that was worn-out.
Now replace the copular verb - was - with other copular verbs, like seem or become. It is still grammatical, and hence worn-out is not verbal, instead it is adjectival.
These socks are worn-out.
Here the same way, we can judge that worn-out here too is adjectival. Just replace are with seem or become.
Something worn-out deserve to be thrown out.
Here the pronoun something is being post modified by an adjective worn-out. We can also re-write this sentence this way -
Something (that are) worn-out deserve to be thrown out.
Here like the previous case, replace are with seem or become. And hence it is Adjectival, and not verbal.
In all the above cases, worn-out is adjectival. And it is formed by the past participle form of the verb wear and a preposition out. It has two lexical bases. And it can be considered as a Compound Adjective. [Reference - Page No. 535 of Biber et al.]