There comes a point where the center of the patch starts to cup upwards and you are rolling on a donut rather than slice of bread. I haven't done this yet, but you can find it by stamping a sheet of cardboard with the tire at varying pressures. On 35s on a typical TJ, my understanding is that this occurs a little below 8psi. Meaning that 8psi is right about the lowest one should go, +/- a bit.
Something I have noticed on mine over a few sets of tires is that below 8psi the sidewalls get too squishy and there is a lot of lateral movement that I don't like.
Once I switch to 17s and install the Coyotes, I expect a few very interesting things to change with how the tire behaves at low pressures. Less sidewall makes for less lateral movement. And the internal beadlock only allows the tire to squish and deform so much. I expect an noticable increase in stability and tire predictability, especially while on hard off camber leans.