LIES! You want your family back so you can play 'Pokemon'.
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I will fully and happily admit that I would like the sister to be alive to join the harem.
But I agree with
JJDrakken that I haven't seen more than maybe one person ever bring up the mom being alive. It is 100% confirmed that she is dead and gone.
The door has been left open for the sister though. And it wouldn't be hard to bring her back. It's a common plot of soap operas and other stories too. No body confirmed means the door is open for them to come back or not.
MoonBox , as far as I've seen, has always been rather coy about it. Giving winky faces and thinking face to posts about the sister. I think MoonBox enjoys the speculation and also teasing the fans a bit either way. But even a subpar storyteller could easily bring the little sister back.
Her having survived but lost her memory being the quickest and easiest. But there are more creative ways too.
You could point to the MC saying that his mother had her arms wrapped around a body, so who else would it be but the little sister, but how does he know that? He wasn't there, he didn't see the bodies. He was likely told that by someone else, who also probably didn't actually see the body. He doesn't know that she was sitting between them. She could have been by the window or in an aisle seat. She could have gone to the bathroom before the crash and someone else could have ended up "in the mother's arms" as they were tossed around the cabin of a crashing airplane. That is if anyone was "in his mother's arms" at all and he wasn't just told that to help him cope and move on. We also don't know the specifics of the crash if I'm not mistaken. Do we know if it was over water or land? Was it a fiery crash or did the plane crash relatively intact but everyone still died? Rescue/emergency crews wouldn't be keeping track of if one body was holding another one lovingly, they would be pulling bodies out and trying to identify them. Any story the MC was told is just that, a story. No one can know if the little sister (or anyone or anything) was really cradled in the mother's arms.
Of course, I am ready to accept that my hope is slim, that the sister is likely not coming back. But there is nothing in the story that prevents it from being possible. It all hinges on what MoonBox wants to do.
I also still hold to my belief that
if the sister is alive with memory loss,
and we have met her, then she is Polly. Dyed purple hair (hiding her natural blond), she is the correct age, has the correct eye color, and is one of the few characters that the MC didn't instantly win over.