Your story makes me think an egg predator suddenly showed up. Most critters that eat the eggs leave evidence behind, either egg shells or wet spots in the nest. In Virginia the ones that immediately come to mind are raccoons, possum, skunks, or maybe even the chickens themselves. Rats should not eat that many at a time. Sometimes the hens will clean up the egg shells but from what I've seen they are not always perfect when they do that. Have you checked closely in the nests for any evidence.
The molt is a main cause of hens not laying, but if that were the case you'd see a lot of feathers flying around. Besides, the molt is not going to hit all your layers in one day. Same thing for hens hiding a nest. That's a very common cause of you thinking they stopped but not all of them overnight. Highly unlikely.
In Virginia I'm aware of three things that take eggs without leaving evidence, snake, canine, and human. I've had snakes eat eggs before. One shows up and eats eggs (how many depends on the size of the snake) then it goes away for two or three days to digest them before it comes back. I had a 5' black rat snake eat eggs out from under a broody hen. It ate four eggs the first time and came back three days later to eat more. If it is all of your eggs every day it's is not likely to be a snake.
Most canines like a fox or coyote would more likely to be interested in your chickens instead of the eggs, though they will eat both. However a dog will often eat eggs and not bother the chickens. Does a dog, either yours or another one, have access.
A human doesn't necessarily mean a thief. Some people have been known to play practical jokes of this type.
So what can you do. If you can lock them in a coop/run a couple of days instead of letting them free range, see if eggs start to show up. That could mean you are keeping them from laying in hidden nests or you may be locking an egg eater out. Or take a couple of sacrificial eggs and discretely mark them. If they disappear something is getting your eggs. This may allow you to determine if they really have stopped laying.
Good luck. This type of thing can be very frustrating. Many of us have been there.