Battery Protection IC: How to ensure that even under-voltage batteries are allowed to be charged?
This would largely depend on the chip you're talking about (next time, maybe links?)

But most implement a back-to-back MOSFET, either internally or externally, where UVLO (under voltage lock-out) disables one MOSFET and OVLO (over voltage lock-out) disables the other, like so:







simulate this circuit &ndash; Schematic created using CircuitLab

As displayed in the image; D1 is the internal Body Diode of the MOSFET M1, and so D2 is inside M2. They are a given.



If the chip sees 2.5V or lower on Vbat it will turn off M1, this will block current going out, but the body diode will always allow current in, as long as M2 is turned on.

If the chip sees 4.25V or more on Vbat it will turn off M2, whit will block current going in, but the body diode will always allow current out, as long as M1 is turned on.

Of course the chip would prefer to always have both MOSFETs on, if the situation allows, because they usually have lower voltage drop at operational current than the diodes, but even if it takes a few seconds to turn a MOSFET back on, the bode diode will always allow current to flow in the other direction.

Many chips also have a Vout line to sense the voltage drop across the MOSFETs, allowing it to turn off for a few ms to a few seconds when it is higher than a given voltage. This allows an engineer to select two MOSFETs with an On Resistance such that a specific current limit is set.

For example if both MOSFETs have 50 mOhm on Resistance at the working voltage and the chip senses a limit of 100mV. The two MOSFETs together will have 100 mOhm, 100 mV over 100 mOhm will yield a current limit of 1A.