"Cut off from the Force" and "entirely completely disconnected from the Force overall with no remaining connection to it at all" don't exactly mean the same thing, Star Wars is confusing. There's stuff to suggest that everybody would die everywhere if the Force was destroyed, because it isn't limited to just the Star Wars galaxies and their satellites—the Yuuzhan Vong, for example, were specifically cut off from the Force by their home planet because they were too hostile and warlike.
Cut off, not entirely removed. They were still able to be affected by some effects of the Force, and some of them still ended up having some sort of reconnection. I think it's overall presented a bit more akin to being actively severed from any ability to control or use the Force, just a bit deeper.
But there's also stuff that can be taken to suggest that not everybody everywhere would die if the Force was destroyed, just a significant number, or most. Everything that lives is connected to the Force in some manner in Star Wars, the Force essentially being the wellspring of life as has been presented various times. You can suppress it, but we've never seen anything or anybody entirely removed from the Force or having their connection to it drained in totality without them dying outright. Even one of the closest we have seen, the Jedi Exile, Meetra Surik, was still able to form Force Bonds, was still able to eventually control it again...yeah.
But it's also a bit of a pointless thought exercise to begin with because it's never going to happen either on this site or in any actual canonical Star Wars media, given that the Force is such a massive, central part of the entire setting.