no, the BMS doesn't take the charge and move it to another cell, that cell is just overcharged, by about .6V so it may be dead now.
the leds will not tell you it is overcharged. it shoulda been apparent the cell was not connected when you measured the voltages at the sense wire plug initially. should never have gotten to this point.
you should already have sheet with the voltages of each cell written down so you can track them. the voltage shoulda dropped rapidly if it was connected to the shunt resistor, so not sure why it took so long. you may still have bad wiring.