This exercise is a good example of the recurring ugly problems with the Korean course once you get past the first two levels.
I first wrote "still living man" - that was rejected because Duo wants a relative clause. The next time I wrote "a man who is still living" - that was rejected because Duo wants "alive" instead of living. Then I wrote "a man who is still alive" - that was rejected because Duo wants "the man"
It's ridiculous. I've lost count of how many times I've had an answer rejected because I put the "wrong" article when there aren't any articles in Korean in the first place and any noun can be plural even without the 들 marker.
아직 살아있는 남자 = [The/a] man who is still alive
Only if wished to stress
▪ "a", as "some/a certain", use 어떤
아직 살아있는 어떤 남자 = Some/A man who is still alive
▪ "the", as "the aforementioned" or as "(shared knowledge) the", use 그, that
아직 살아있는 그 남자 = That/the man who is still alive
있다 is 'to have' or 'to be in a location' 살다 is 'to live' combined as 살아있다 they're 'to be alive' or 'to be living' The 는 particle in this case shows that the verb is describing the man. 살아있어요 = '[I'm] living' 남자는 살아있어요 = 'The man is living' 살아있는 남자 = 'the living man' This one is not a complete sentence and would be followed by another verb. (eg. 살아있는 남자는 밥을 먹어요 = The living man eats a meal')
It's not a relative clause in Korean, that is just the only (obvious) way to translate it into English. It is a Modifier in Korean. Check out the Tips and Notes for the modifiers lessons and they explain how modifiers may be translated into all sorts of which/who/that/etc. sorts of clauses. All of this has been introduced.
To give a brief explanation here, Korean modifiers are like turning whole sentences into adjectives. If the "sentence" turned into a modifier consists only of a verb (especially a descriptive verb) then you can usually translate it as an adjective in English. For example, if we just referred to 살아있는 남가 then the Modifier form of 살아있다 (to be alive/living) means that 남자 is described as someone that is alive. This being a single verb which has a good participle adjective form in English, we would probably translate it as "A living man" rather than "A man who is alive." But when you expand the Korean modifier beyond a single verb, describing the man as "still alive", it is no longer as natural to try to use an adjective. It could be done, by saying "A still-living man", but that sounds like it could mean something complete different from what is intended (especially in spoken English where you can't see the hyphen, it sounds like the man is still as in motionless, but alive). Trying to translate it as an adjective just doesn't work very well. So we have to use a who clause instead.
Sometimes you can translate multi-word modifiers as adjectives, it just doesn't work well in this case. For example, an 아이를 먹는 괴물 could be translated "a monster who eats children", or it could be translated "a child-eating monster". 책이 없는 도서관 is "A library which/that doesn't have books" but in this case the preposition "without" translates it more naturally than a clause or even an adjective: "A library without books." (I suppose you could try to invent an adjective to use: "A bookless library"--that doesn't work with this example but you could use that sort of construction when the noun is something other than book, like fear -> fearless.) Sometimes modifiers ending in 있는 are translated "who has" but sometimes "with" is more natural, and sometimes adjectives are created, like "A one-eyed, one-horned, flying purple people eater" rather than "A purple thing with one eye and one horn that flies and eats people."
Long story short, because modifiers are a grammatical construction that has no exact English equivalent, we instead tend to use whatever English grammatical construction is best suited for the particular case. And of course, check out the Modifiers lesson/Tips and Notes for a refresher.
No. That would be a clause with Subject + verb + complement.
남자가 아직 살아있어 - The man is still alive.
Here we have an adjectival clause i.e. one that acts as an adjective helping to describe a noun. So the example given is actually a phrase (Adj + noun). There is no main verb involved.
아직 살아있는 - (still living/who is still alive) Adjective/adjectival clause, used to modify the noun 남자 (man). So the correct translation has to be: "The man still living (or who is still alive)".