And for the record, as F&P explained, and I explained, we know this did not happen with their cells because all of the lithium salt they put into the cell was still there after the boil-off.
You are confusing foaming with liquid entrainment, or any other liquid loss.
Foaming doesn't necessarily implies liquid loss, so it doesn't affect the salt balance after the boil-off. Therefore the recovery of the all of the lithium salt at the end of the boil-off doesn't exclude the formation of a lot of foam.
However, foaming is able to explain in a straight mundane way the rapid decrease of the apparent level inside the four cells, which was documented by F&P in this video:
More precisely, this decrease is due to the rapid deflation of the foam, which progressively built-up during the final boiling phase, lasting a few hours. This foam was highly inflated by the intense generation of steam bubbles in the very last minutes preceding the complete boil-off of electrolyte, as it was better described here: FP's experiments discussion