Just tested again, I got caught 3 times into a latex bed while on floor 1, at no point did I get dragged down pink stairs. On the 3rd bed, it was game over, not even "Press E to struggle". On another run, at a latex floor (5F), I got caught, screen fade to black, it fades back in in the same spot, I didn't get moved at all. I get caught again, game over.
I also noticed that the "spend 1 turn in X jail" outfits don't unlock by actually being sent to said jails. Did you mean "escape X jail 1 time"?