There are so many reasons how a cell becomes faulty and lots of different ways they behave when faulty. Some go weak, some self-discharge, some lose capacity, some get high resistance, etc. That's why it's not a good idea to use used cells. You have no idea what they're like unless you test for all those things, which will take forever, and most will fail one of the tests. Voltage and capacity measurements are not enough on their own. You have to do load tests, self-discharge tests and measure internal resistance.
Obviously, if one cell is self-discharging, it will drag the whole string down.
There is virtually no charge in a cell between 1v and 3v, so within a few seconds of charging a 1v cell, it will spring back to life. It works the other way too, which is how they get to 1v. Somebody runs them down to 3v, then doesn't charge them. the smallest amount of self-discharge, which many cells do, sends them down to 1v. You wouldn't notice self discharge when the cells are properly charged because it takes a comparably massive amount of discharge to go from 4.1v to 4.0v.
Cells that have been down to 1v will never behave like new cells, and are not suitable for ebike batteries, so keep them for lights and power banks.
You will soon learn that all this messing about with used cells is a complete waste of time, like we told you in the beginning. I guess that you're already starting to figure that out from the experiments and tests that you've already done.
The only time it's worthwhile is if you can get hold of relatively new, but faulty ebike batteries. I got one recently that had 50 cells, but one string was down to zero volts. I hoiked them out and reconfigured it to a 40 cell battery with a new BMS, which should give years of service. I put a new BMS in because the most likely cause of the string going down was a stuck open bleed resistor.