@arteteco I can not give you an example of something that is both true and unfalsifiable, not if your criteria for true is something you can test against (provide evidence for). But just because it is impossible to prove something to be true, does not mean it isnt.
Take the general idea of a god, not related to any one religion. But the nature of god (As someone or something that is all powerful) it is unfalsifiable since any god figure that had that level of power could easily change all the evidence in the universe to whatever he wants.
So if logically reasoning about if a god were to exist the conclusion must be that unless god wants there to be evidence, there will be none.
Now I'm not saying that is a good enough reason to believe in god, but it does provide you an example and explanation as to why something could be true and unfalsifiable.