Let’s clear up some misconceptions people have about LiIon and LiPoly batteries.
1) Almost all LiIon/LiPoly batteries have a protection chip inside them that no-longer lets the battery power devices when the Cells voltage reach a certain level. The most common cut-off voltage is 2.8V but can be much higher in certain applications.
2) Even after the protection chip cuts the cell off due to low voltage the CELL will continue to discharge at ~1-10uA. As a result eventually the CELL’s voltage can reach 0V if not charged.
3) Unknown to most is that if the cell reaches 0V it CAN be recharged.
3a) Letting the cell reach 0V can permanently reduce the CELL’s capacity.
3b) Most protection cells are not designed to let the CELL be recharged after the cell’s voltage is below 0V.
4) Storing cells at around a 3.8V charge will achieve the longest lifetime and output of the battery.
4b) Storing at 3.8V also gives the cell plenty of headroom for self discharge. YES, a LiIon battery sitting by itself will discharge on its own.
5) Charging most LiIon batteries to 4.1V will give its longest lifetime (Non-Panasonic Cells).
5b) Charging most LiIon batteries to 4.21V will give the batteries the most output per charge but will decrease its lifetime (Non-Panasonic Cells).
5C) Panasonic Cells can be charged to 4.3V and is part of the reason they can have the highest output on the market.
5D) The same protection circuits that keep cells from over discharging also will prevent the cell from being over charged. Usual cutoff is 4.2V.
With all of the above being said, there are lots of considerations and tradeoffs in the design and use of LiIon and LiPoly batteries. Most batteries on the market will not let the cell be charged from 0V because it is the cheapest protection chip available.
5+ years developing commercial products with LiIon and LiPoly batteries.