If they're Lithium Ion cells that are not LiFePO4 or LiTi, then <2v is typically empty, probably below the zero capacity spec of the cell. randomly chosen from google search for cell spec sheet
declaring minimum voltage as 2.5v for that cell.
The cells I use EIG NMC C020
state minimum 2.5v as well.
Other cell spec sheets may differ, but all the ones I've looked at over the years are above 2v.
The BMS should be shutting off output well above that, often around 2.8v, sometimes higher.
LiFePO4 and LiTi are lower voltage types of cells, so the above voltages don't apply there.
For now, there's no way to know (without destructively opening up the cell and examining it microscopically to see if there is damage to the internals) if a cell has damage from overdischarge or not. Maybe someday someone will develop a characterization tool that can tell from the externally available properties whether a cell has specific types of damage.
Without bieng able to tell, it's safer not to use cells that have been overdischarged below the spec sheet values.
Up to you what you want to do, but I would not recommend it, simply because the results of a fire are very bad, even if the risk of one is very low.