I don't know of any consumer device whose lithium ion (not LiPo, whole 'nother kettle of RC hobby danger) is allowed to discharge to a damaging level before shutting off. Running the battery from full to fully discharged (according to the device, probably still 15+% actual remaining) is, in fact, the only way to get the "life meter" calibrated on most devices, one of the reasons companies like Apple recommend a complete charge/discharge cycle every month or so.
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