Totally depends how tight the tyre is on the rim/rimstrip…
I've got 2.35 Bontrager ACX's on one of my bikes, setup Ghetto. Now these are proper "Tubeless ready" tyres (ie. they have a tight bead) and were an absolute arse to fit. I would say I've run them as low as 20psi, and trust me, there's no way those tyres are coming off the rim unless they're prized off with BIG tyre levers once totally deflated! You can have a go yourself if you want to try and dislodge them, but they're locked on there!
Other tyres I'd still be careful with 40psi in because of looser or weaker beads.
My view on the whole tubeless thing (aside from the fact it works, and I don't like inner tubes!) is that you're best off buying stuff that's been designed to be run tubeless in the first place, especially when it comes to tyres. You'll have much less faff in the end… But Ghetto can and does work with the right tyre/rim combinations.