Are all the BMS built the same way?
I have seen some batteries where the bms only looks at arms or segments we could call it. So you may have 4 or 8 cells it looks at as one entity. no NOT the best way to do things. Still, yes you may get your pack back working but it's going to be overall degraded because the new cell can't be used to it's max because of the older ones. They lose capacity remember, so the entire pack may be down 15 percent. wel 14.7 now with the new cell.
As with most cells, pushing them to their very tippy tops or bottoming out on them, shortens their life too. So if the battery is terminating it's charge, because the cells are tippy top time and time again, it's shortening their life span. A battery pushed to a full 100 percent duty cycle may have 1000 cycles in it. if you were to cycle it 80 percent, say, shaving 10 percent off the top and bottom, you may get 3000 cycles out of it, if you were to drop it to 70 percent, again shaving the ends, you may get 5000 or even 10k cycles out of it. Some of the so called 'better' batteries out there, prolong their life cycles by actually squeezing an extra cell or two in there, so the voltage is by design, cycling in that 70 to 80 percent range. I may call it a 72 volt battery, even though by build it's really an 80 volt battery. I just have you charge it in the 72 range which is the EQ of a 70 percent charge cycle, to prolong it's lifespan.
Aaron