Pop N Wood

There is little that a BMS can do if a battery cell shorts out internally. The current starts flowing inside the cell, it gets hot, causes the cell next to it to overheat and in turn break down/short out, creating more heat and eventually a fire. Hence the moniker "thermal runaway". Once a cell shorts out, it is going to keep arcing until is expends all the energy stored inside of it. All one can do at that point is cool the battery pack to keep the burning cell from taking other cells with it. Hence the reason airline attendants are trained to drench an overheating lap top with water, cool it down and stop the thermal runaway

It can happen to even the best of batteries, really doesn't matter who makes them. A quality battery will have a much smaller probability of it happening. Manufacturing tolerances, impurities, poor manufacturing practices, and any sort of physical damage can all cause a cell to short out internally.

To the OP the BMS can't "increase the current" to supply more current as the battery is depleted. Whatever juice the battery can supply is a matter of physics. If a cell is depleted or dead, the internal resistance increases limiting what it can put out.