そんな事で変わる未来じゃないだろう where's the subject

Question

I'm reading the manga Orange and one of the lines that's said by a character is

「転ばないよう気をつけろ」なんて言っても、そんな事で変わる未来じゃない

So far, my understanding of the sentence is:

転ばないよう気をつけろ」なんて言っても
Even if we tell (him) to be careful not to fall

The next clause is where I get a little tripped up:

そんな事で変わる未来　じゃない

The translation from the anime is "we won't be able to change anything." So the question is more of a grammatical question, not so much a translation question.

It's saying that the "(Something) is not the future that will change by doing that" but the (something) isn't specified. What is that something? In other words, 何が　そんな事で変わる未来　じゃない？

In a simpler example, if I say 明日食べるケーキ　じゃない and there's a cake in front of me, then the meaning is clear: This cake is not the one I'll eat tomorrow. So is the same grammar logic happening in my manga sentence, and there's an implied subject that's happening somewhere in the conversation?

Answer 1

I think you can read it like:

「転ばないよう気をつけろ」なんて言っても、 （そんな未来は） そんな事で変わる未来じゃない

(That kind of future) is not a future you can change just being careful.

Answer 2

I read Wikipedia about a manga Orange. This is science fiction. The main girl character received a letter from what she will be in ten years. It was written on it that a boy who she likes will die after a year and that she should act to prevent his death. So I think the omitted subject is "彼が死ぬ未来(the future that he will die)".