Use of should

In the first sentence, she has not died yet. She is alive.
in the second sentence, she died.

We use "should have" to talk about past events that did not happen.

I have to disagree with Anonymous on this. In both versions "she" has, in fact, died. As to the difference in meaning there really isn't any. I'm not sure I can state why a speaker or writer would choose one version over the other. My best guess is that the first is a way to kind of draw attention to the statement while the second is just a routine comment.

Hello

The simple answer is: nothing really.

The modal verb 'should' is often used to add a personal opinion about a fact (she should/should not have died). But the clause 'It's unfair' does the same thing, so the end result is two sentences meaning the same thing.

Best

BillJ

Debpriya De"It's unfair that she should have died so young". If we rewrite this sentence as "It's unfair that she died so young", how will the meaning of the sentence change ?

Your rewrite will make the statement more matter-of-fact. The original strikes me almost as a comment on the unfairness of the world in general as exemplified by this particular example