A broken sense wire from cell to BMS means the BMS won't be able to read that cell group's voltage.
If the BMS detects a problem with the pack, such as a cell or cells that are no longer matched with the others, or overcahrged or overdischarged, it will turn off the output and often the input to protect the packs against damage that can lead to a fire.
Some BMS that are poorly designed can't tell a sense wire is broken and will read that as a functioning group with whatever voltage is detected and/or it just ignores the group, which can lead to actual cell damage and eventual catastrophic failure in worst-case scenarios. Yours has probably shutdown because of the broken wire. Before trying to fix it:
If you are *certain* the cells are not damaged, and they aren't overcharged or overdischarged, you can troubleshoot the pack and repair it. to make sure they aren't:
The first thing to check is each of the cell (group) voltages, starting at the most negative one, and listing them so you can see them all next to each other. If they are not identical, then the pack is imbalanced, which means that the cells are different in characteristics from each other, and will perform differently. If they are *really* different, by more than a tenth of a volt, the BMS may have shutdown just because of that.
if any are above full charge voltage for that cell brand/model, or below empty voltage, they are damaged and the BMS shutdown because of that. What that damage is and whether it is dangerous is impossible to know until something catastrophic happens, which is why it does this, and why it is not recommended to try to recover such cells.
Once you know what voltages the cells are at, then we can proceed with what to do from there, such as figuring out the physical cell configuration so you will be able to reconnect the wire, etc.