Comma before a clause without an explicit subject

[Natalia]

Is it acceptable to put a comma before a clause without an explicit subject?

For example:

A good teacher presents material in an amusing way, cares about a positive atmosphere in the classroom.

The sentence above is taken from my notebook, and I am curious whether it is grammatically correct.

[Daniel]

That's awkward, and it's not a 'clause'. It's asyndetic coordination (coordination without AND), which works marginally in English when you have a list, or almost as a sort of appositive (which is a normal and acceptable use of a comma):
A good teacher present material in an amusing way, makes her students laugh!
What I just wrote is sort of a renaming (appositive function) of the first part, so this is acceptable with the right intonation (but hard to convey in writing).

In the original sentence, the comma doesn't really make sense to me. I'd call it a typo.

[Natalia]

So I may use the appositive to clarify a sentence it precedes?

Is it corrrecto to write:

Students are engaged to produce some language, use words/phrases they know to express an idea.

[Daniel]

Maybe. It's awkward. I'd avoid that in formal writing unless it is very clear contextually. Even if acceptable it's somewhat poetic. Avoid it if in doubt.
(But yes, technically, that's an example of the structure.)