There is 80% charge and there is 80% charge.
Electronic equipment (cell phones, laptops, etc) require a certain minimum voltage to be able to function. Simpler devices, like flash lights, can function down to near zero charge (albeit whether usable is another question)
When manufacturers state that a battery should not fall below 80%, they talk about the kind of depletion that you get when you use a battery till it is completely flat, eg due to a continuous drain, such as by flash light globe.
A cellphone, or laptop however would cut out long before this... probably even before a battery reaches this 80% limit. This is due to the internal resistance of the battery going up, which causes a voltage drop under load. If the battery is near enough to fully charged, e.g above a certain threshold, this voltage drop doesn't show up when using a simple meter to test battery charge, as these meters does not put enough load on the battery to cause the internal resistance to have a real effect.
Cell phones and such have "intelligent" managed batteries to be able to report to you how long you can still use the battery, e.g before it reach the threshold where the internal resistance causes the supplied voltage to go too low to be able to power the device.
So there are two measures of battery charge:
- That reported by the battery indicator on the cellphone is "time until battery reaches cut-off threshold"
- The actual amount of charge resident in the battery, regardless of whether it can be used by a specific device.
This complicates the whole situation: How do you control the device to not use the battery below a certain threshold (Type 2 above), when that threshold is measured on a different scale compared to that reported by the battery level management circuitry (Type 1 above)
I'm quite sure there is no way to do this, but in all likeliness your device will never deplete the battery to below the 80% manufacturer safety margin, so this is not a real issue.