How does a battery balance and protection circuit work?
I've read a chapter from a very good book which answers it all.
I highly recommend reading that chapter or the book but if you want the very short story things are like this.

Normally it is assumed that a pack is assembled with balanced cells thus a regular BMS is not designed to balance huge differences.
Normally lithium cells have a very low self-discharge rate and are quite evenly matched so only minor balancing is required to keep the pack in good working order.
Most BMS boards that have balancing only pass a very small current from the most charged cell to a shunt resistor thus they effectively waste charge until the other cells get to the same level.
Most balancing circuits don't pass current from a cell to another (active balancing) because it's more expensive to do so.
Depending on the charging circuit, balancing is not active all the time but might be active only during the and of the charging. Since a large imbalance should not happen it would be stupid to waste energy from a more charged cell when the pack is disconnected from the power supply.
It takes many cycles to balance the cells. Of course, depending on the circuit things might vary but you could expect to balance a 10% difference in 30 or so charge cycles.
The imbalance per cycle of properly matched LiPo cells is usually less than 0.1%

This simple balancing technique which is most likely implemented in common BMS boards works like this:


The  internal  balancing  P-MOSFET for a particular cell, which needs to
be balanced, is turned on first.
This creates a low-level bias current through the external resistor
dividers, which connect the cell terminals to the battery
cell balance controller IC. The gate-to-source voltage is thus
established across R2, and the external MOSFET is turned on. The
on-resistance  of  the  external  MOSFET   is  negligible
compared with the external cell balance resistance and
the external balancing current, I BAL , is  given by I BAL  =  V CELL
/ R BAL . By properly selecting the  R BAL  resistance value, we can
get the desirable  cell-balancing current, which could be much higher
than the internal cell-balancing current and can speed up the
cell-balancing process. The drawback of this method is that balancing
cannot be achieved on adjacent cells at the same time.