This one is a bit tricky, in fact. What it means to say in English is “when the coffee is empty, we won’t refill it”.

In Japanese, instead of こちらのコーヒーが it should say こちらのコーヒーは. With the は it’s correctly implied that the こちらのコーヒーは refers to 終了になります, therefore “the coffee is over (when it’s empty)”. With the が, even though the mistake is obvious to an experienced speaker, it could be theoretically implied that こちらのコーヒーが refers to なくなり次第, therefore leaving the subject to 終了になります vague/dangling: “when the coffee is empty, [something else] is over”.