No, but that doesn’t really matter - the く form makes it into an adverb, meaning it will always modify something else (a verb or another adjective). You won’t ever see a く form as a predicate, only ever as part of one or part of something that isn’t a predicate at all.
Also I looked it up quickly: technically there’s no copula included in い-adjectives at all, but い-adjectives are (in origin, anyway) verbs. It’s just that their meaning includes the meaning of the copula (i.e. ascribing a quality to a noun). So there’s no copula involved in the first place (I thought there was and い was some antiquated copula as is the case with な, but I was mistaken).
Okay, so take the sentence “これは赤い車だ”.
The subject is これ. The thing you’re saying about the subject is 赤い車だ - this is the predicate. In this case it includes a copula (だ): this is a red car.
Let’s rephrase the sentence into “この車は赤い”.
Now この車 is the subject, and the predicate is 赤い. You now no longer have an explicit copula in the form of だ, but it’s still technically part of 赤い - you can see it in the translation too, “this car is red”.
Now let’s say something else: “この赤い車で運転した”.
The subject is now no longer part of the sentence. It’s implied to be me (unless context implies otherwise), and the entire sentence is the predicate - or in other words, I’m talking about myself and the information I’m giving you is “I drove this red car”. You’ll also notice there’s no copula in there. Instead, we have a verb.
Now, say you want to confirm: “この車?”
Now we don’t have a predicate, only a subject (this car). However, the predicate (i.e. the question “is this the one you drove?”) is implied, and immediately understandable through context, but not explicitly stated.
And if I confirm: “そう!”
Now we have neither. We have no subject and no predicate, essentially the entire statement I’m making is implicit, and そう defines it as “whatever you just said” basically. So I’m implying the entirety of “I drove the car you just pointed at”, but I’m not actually making that part of my sentence.
(as a technical detail, I think そう is technically part of the predicate as an adverb, but I’m not 100% sure of that)
With all that said, this is nice to know about but not really something you need to concern yourself with. It’s basically a long-winded way of saying “you’re always conveying some information, but the parts of that information that are already clear are left out, with no restrictions on which parts of a sentence always need to be present”. That’s all you need to worry about.