In English, you can say "My cousin is sick." And that sort of conveys a lot. Your cousin could have cancer and be terminally sick, but could also be crazy ("sick" as in slang for cool), or sick as in disgusting, but also could just have the common cold.
By saying something like "Before my cousin got sick, blahblah," and I think that heavily implies your cousin has been sick long enough for there to be a "before" and an "after." Does this make any sense?
But in Chinese, how would you indicate that someone is terminally ill? Like, you don't want to be specific and say they have cancer/other illness, you just want to say that they're sick and IMPLY it's terminal, without explicitly saying so.
TL;DR: I know when someone is sick you can differentiate by saying 她感冒了， 她发烧了，她生病了, etc, but how do you imply someone is terminally ill?