Lihtium Ion cells are depleted at 3.0V, not 3.6V. The 2.5 is the lower threshold after which you should no longer use the device without replacing the battery. Most if not all BMSs on the market are well aware of these data points and will respond accordingly: hard shutdown at 3.0V, after that they will use a few uA until you charge them and around 2.6V they go into 'deep sleep' which means even indicators and other interaction stops until the device is recharged.

It is very hard to get a device to go below that 2.5V, unless you aim for it by leaving it for many months (and with slightly larger cells years), self discharge at that voltage is extremely low unless the cells have been damaged.