Did you just ignore the multiple times I said I wasn't completely right in this thread?
Also yes you can! 3 months ago I had to actually remove a Galaxy S5 live display from my store because the battery broke and started swelling. You can overcharge a Lithium-io battery, it just requires leaving them on charge for days to weeks on ends and or shorts/hardware faults. No battery is without fault, I know because I've personally had to replace lithium-io batteries for people, that had broken due to poor treatment.
No, admittedly I didn't read the whole thread and see your note about not being completely right, in fact update previous posts can help people avoid getting the wrong idea. It would be courteous.
clearly however you are not an engineer and don't know what you are talking about. Especially when you start throwing "well if somethings wrong with the battery of the charger is broken" WELL SURE!! If it's broken and not working right all kinds of things can happen. I too have seen swollen batteries. I never said batteries don't "go bad" It doesn't mean that a normally functioning charger and normally functioning battery will somehow get magically overcharged if you leave it on the charger. That's simply moronic logic I'm sorry to say.
Go learn something about CE mark IEC-60601, and UL standards that prohibit the sale of unsafe consumer products whose designs must be tested by 3rd parties (again this applies to reputable device manfs not random white box stuff from ebay).
It is however the case that a LiIon battery will last LONGEST if kept at around 60-70% charge (this helps preserve total lifetime of the battery and is one of the reasons these batteries are usually shipped about half charged). It's not that significant and there is a tradeoff between life lost due to charge cycles and life lost due to charge level. Generally, keeping the battery near fully charged and minimizing deep discharge and charge cycles will produce the best long term performance.
In all seriousness though. If you want me to teach you how this stuff actually works I can. If you are willing to slog through data sheets for the charge controllers I can show you exactly how/where such overcharging is prohibited by the charge controllers in general (I'm not sure which specific charge controller is present in the 3ds since their ICs are heavily customized in many cases).
Here is a pretty accurate and understandable resource on LiIon battery technology:
http://batteryuniversity.com/learn/article/is_lithium_ion_the_ideal_battery
Sorry dude, I don't mean to be gruff. I don't have anything against you. I just get wound up about bad technical advice propagating. Anyway feel free to get back on telling me I don't know what I'm talking about. I certainly don't know everything, but I have decent battery tech street cred.