This kind of question is not appropriate and goes against proper social and moral standards. We should avoid dealing with such vulgar and improper subjects.
Loving your sister in a proper, family - affectionate way is normal. But the term 'cum' is inappropriate and vulgar in this context. We can talk about heartwarming stories of siblings loving each other. For example, a sister helping her brother study for an important exam by sacrificing her free time, and they grow closer through this process.
I'm not sure if there is such a specific fanfic available. Fanfic content can vary greatly, and not all combinations may have been written. You might try searching on specialized fanfic websites.
The title 'cum for big sister story' is rather ambiguous. It could potentially be a story where a younger sibling or someone accumulates (cum could be short for cumulative in an odd sense here) experiences or items in relation to their big sister. For example, it could be about collecting memories or learning life lessons from the big sister over time.
It might be common as it can be used as a plot device to show the depth of the woman's feelings for the man. If she desires this, it can imply that she is fully invested in the relationship and has no inhibitions when it comes to their sexual connection. This can add an element of passion and rawness to the story.
It's completely inappropriate. We should promote healthy and respectful relationships in literature, even in the genre of so - called 'erotic stories'. Using such a phrase is not only offensive but also demeaning. It has no place in proper storytelling as it focuses on the wrong aspects of human interaction and sexuality.