What is the interpretation of "which" in this sentence

'It' in 'when you pay attention to it' doesn't naturally refer to 'the fact ...', only to 'a story', so 'which is interesting when you actually pay attention to it' attaches to 'a story'.

In 'every human has a story', 'a story' is synonymous with 'a life history': the implication is not 'at least one story'. So 'which is interesting ...' is non-specifying (ie not pointing to one particular anecdote among many).

So a paraphrase is:

• Everyone's life history is interesting if one takes the trouble to look at it in depth. This fact means that (if I do take the trouble), I connect better with these people, and with people in general.

The clause is restrictive in that it limits "story" to "interesting." "Which" should be replaced with "that" to clarify.

Analysis considering that this is British English ("which" is not restrictive in American English). (ref.)

Let's consider the sentence without the modifier of "story", that is, without "which is interesting when you actually pay attention to it", a modifier that is defining or in other words, non descriptive, or, according to yet another alternative terminology, restrictive; it is restrictive because there is no comma before "which".

• The fact that every human has a story is something that makes me more connected to humanity.

Can we say that there is anything that captures the interest of the reader in this amputated sentence? Does it formulate as such a really complete thought? Shouldn't we feel that there is something more to that idea? Aren't we left with the question "Yes, we all have a story, but in what is that so interesting? After all, isn't there a considerable number of us to agree that countless is the lot of our personal life stories that have no interest, that are downright boring. So, hasn't this writer something else to say? Is there not something peculiar that is instigating this remark, which does not seem to have been brought to its conclusion? I believe this conclusion is not left to another sentence and that it is to be found in this modifier: it is in all cases, if you pay attention, an interesting story, which is telling us something new, something that we might not be many to realize. I believe that the grammar is a confirmation: "that", because of the grammar, refers to "stories" such as modified in the original sentence. In other words, the fact is "every human has a story which is interesting when you actually pay attention to it" and not simply "every human has a story".