While I did manage to start with just 10.5 volts, if this chart is accurate then it seems that really is the limit.
I think Tim has posted something similar a few times in the past.
https://images.duckduckgo.com/iu/?u=...chart1.gif&f=1
I am certainly not suggesting that relying on a battery with a low SOC is a good idea.
I remember being astonished the first time I saw Tim's chart at how much a battery is already down by the time it gets to 12V.
As I said, I understand that you want to know what is going on. While 11.9 volts may not be a problem, the question is how much lower would it let the battery get if the cut out is not doing its job.