This is correct with unmanaged batteries. Batteries with a BMS however will never get below whatever voltage is set as their 0% unless allowed to sit at 0% for long enough that e n t r o p y occurs and the charge slowly dissipates over time. This will happen even with a fully charged battery left to its own devices (ba dum tss) for too long.

The point of the BMS is to manage the health of the potentially dangerous lithium batteries, and as long as they are used within spec it should keep voltages from getting so low the batteries enter a state of deep discharge, as well as prevent overcharging due to imbalanced charging rates or other similar issues.

Used is the important word here. A battery must be used to maintain it's health. A battery must also not be abused to maintain its health.

Now none of that touches on what you said, but was important background for this to make sense: The BMS will report to you whatever values it deems safe charging and Discharging limits based on factors like internal resistance and temperature. As a result 20-80% of an unmanaged battery is close to 0-100% of a managed one in new condition because the BMS will cut power before unsafe discharge limits are reached, and will stop charging to prevent overcharge once those limits are reached.