The motivation has little to do with capacity gains (which will be minimal). Rather (near) zero-volt storage greatly increases safety (e.g. it increases thermal runaway threshold temperature and greatly decreases amount ofrunaway gas production, and eliminates all toxic gases, etc), so e.g. they can be shipped much more safely.
Well, safety is certainly important too, and as anyone who spends much time here learns, there's a lot you can do to observe proper battery safety and charging discipline. But you're more likely to get run over crossing the street in broad daylight than to have a lithium ion battery incident—even if you're in the habit of abusing your batteries—which I don't—although of course certain chemistries are more tolerant than others.
So (not having read any articles yet, but I will), I assume we're talking about current lithium ions of some sort? NiMH batteries, by comparison, are already able to be completely discharged, IIRC.
A brief search turned up this approach for a zero volt capable lithium ion battery:
[FONT=museo_sans300]"Thus, modifying the amount of reversible lithium in a cell with anode pre-lithiation is a promising concept to achieve lithium ion cells with high tolerance to near zero volt storage without modification to typical cell construction parameters or use of unconventional materials."
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https://pubs.rsc.org/en/content/articlelanding/2016/ee/c6ee00836d#!divAbstract
Is there some reason pre-lithiation wasn't done before?
Also, I'm not sure I'm understanding how pre-lithiation works. Are they saying that using this approach, discharging to zero doesn't generate much heat or hydrogen gas, etc? If so, it sounds like not much real work is being done during that phase, otherwise there would be more heat generated and released. Hence, there's very little increase in energy or capacity (as DIY explained), but the battery still has the capability of going to near zero, to take advantage of those beneficial effects. But I'm not sure I'm understanding this correctly.