Jeff, and Katy, it's probably CHF. (congestive heart failure) These big gals are prone to it. They get a lot of fat around the heart, which tends to be too big anyway, to pump blood through such large bodies. It gets so that when they are at rest on their keels, in a normal resting-on-the-ground position, (resting on a roost may help a little, for a short time, but it may not. The body position's pretty much the same) the heart is somewhat compressed, as are the blood vessels. Circulation is impaired. When it gets bad enough, they wouldn't get enough blood to the brain, therefor not enough oxygen to the brain, and they can just die while sleeping.
Have you/did you notice combs looking dark or purplish when the hens were at rest, and returning to normal color when they get up/got up and move around? If so, that's a pretty definite sign of CHF.
When they die of CHF like that, they don't flip. They just die. Flip is when they die of a heart attack, and there's a spasm that literally flips them over on their backs.
Sorry to hear the bad news.