Oh man, that soggy bin feeling is the worst lol. @maryh96 is totally right about cardboard, it's like a sponge for worm juice. Reminds me of the time my friend's bin basically turned into a swimming pool and we had to use a whole newspaper to fix it. Those little guys can really drown if you're not careful.
Cardboard is a lifesaver for a wet bin. I had to mix in a whole bag of shredded egg cartons once to soak up the mess. It dried out in a couple days and the worms were fine.