Hello,
Last night, my brother was playing Smash Bros. for 3DS, and his battery was low. He was just testing out some new custom parts, so he didn't really care. He was in the middle of testing; in the room with sandbag, NOT a menu or a loading/saving screen. The battery died, and he put the system (a 3DS XL, by the way) on the charger. He turned the game back on, and got a message saying his data was corrupted, and all of his data was gone, except;
StreetSmash data; I'm assuming because Streetpass data isn't saved to the cartridge, it was OK.
One trophy, which was Bald Bull. He had that for some reason.
Everything else; replays, records, characters, custom fighters, equipment, everything else was gone.
I told him just to turn off his 3DS and not touch it for now, and we'll figure it out tomorrow. I called customer support earlier today, before posting this message. Didn't help at all. She told us to start up the game again to see what message came up. It was the "Do you want to send gameplay data to Nintendo?" message you get when starting up a lot of games for the first time.
Remember, this is the second time the system had been turned on/game started up since the system shut down. And now it's acting as if there was never any data to begin with, which did not happen the first time he turned on the system since it shut off. My brother selected "No", and then at the title screen, pressed HOME, closed the software, and turned off the system. This happened just a few minutes ago, at the time of writing.
We also looked up this issue online. Other people have had similar issues, but it seems their data was only corrupted if the system shut off while saving. I could be wrong, of couse, but I don't think the game was trying to save during the sandbag test room.
I have a theory that maybe this issue could occur when dealing with the custom character screen at all? There are typically several edits made to a character before being prompted to save and exit to the character select screen. 
So, I was wondering if anybody else might be able to provide an answer as to exactly what might have happened in this puzzling issue, if there is any way to restore this lost data, if there are any steps we should take before starting new data on the cartridge, and if there is any danger of a similar issue happening on either his or my copy of the game in the future (and if so, what precautions we can take to prevent that danger).
Extra notes: Played on a 3DS XL, specifically the Blue Mario Kart 7 bundle, in America (North American system/game/everything).
Bought and started playing the game on October 3rd, the release date. He has been playing pretty consistently since.
Neither I, my brother, nor my brother-in-law (all of which have personal 3DS systems and copies of the game) have ever experienced a similar issue before on these games.
Any help would be appreciated! Thank you very much for your time! 