There probably is. Given the popularity of both Darkseid and Batman in the DC universe, it's a common and rather dark theme for fanfiction writers to explore. Some might write it to show the extreme power of Darkseid, while others may use it as a starting point for a more complex alternate universe story where Batman's death has far - reaching consequences for other characters.
I don't think it's a common concept. Most Batman fans love the character for his moral code which includes not killing. Fanfiction usually tries to expand on the existing lore in a way that is somewhat in line with the general perception of the character. So, stories where Batman kills are more of an exception rather than the norm in the fan community.
Yes, there are some out there. You can start by looking on popular fanfiction websites like Archive of Our Own or FanFiction.net. Just search for the specific tag'superman kills batman' and you'll find a variety of stories. However, the quality can vary greatly from one to another.
It could imply that in some Batman - related fan - made fictional works, there are scenarios where Batman kills, which might be a departure from the traditional non - killing Batman in the official canon.
One common theme is chaos. With Batman gone, Gotham descends into utter chaos as the Joker runs amok. Another theme is revenge. Sometimes the story is about someone seeking revenge for Batman's death. Also, the exploration of the Joker's victory is a theme, showing how he relishes in finally killing his nemesis.
There are some out there. Some explore the dark and twisted nature of such a scenario, delving into the psychological impact on Gotham and the other characters. However, the quality can vary greatly. Some might focus more on shock value while others try to build a complex narrative around it.
In a 'catwoman kills batman fanfiction', the ethical implications are many. It forces readers to consider the consequences of actions outside of the normal superhero narrative. Catwoman killing Batman goes against the norm of hero - protection. It may also bring up questions about the value of a life. Is Batman's life more valuable than the reasons Catwoman might have for killing him? And how does this change our view of both characters in the context of morality and ethics?
Often, there's a theme of justice being redefined. When Batman kills the Joker, it questions the traditional forms of justice in Gotham. It might also explore the theme of power. Does Batman become more of a tyrant or does he find a new way to use his power for good? And there could be a theme of redemption for Batman, as he tries to justify his actions to himself and others.
One possible plotline could be that Darkseid is about to destroy Gotham or Earth in a way that Batman has no other option but to kill him. Maybe all of Batman's usual gadgets and allies are useless, and he has to use a kryptonite - like weapon (if it could affect Darkseid) to take him down.
A common theme is the corruption of the hero. Batman is known for his strict moral code, so when he kills Robin, it shows a breakdown of that code. Another theme could be the exploration of the consequences of power. Batman has a great deal of power and influence, and killing Robin could be a way to show what happens when that power is misused.