Well... they sorta do. Usually if you look at a chicken's dropping on the ground, it'll be a brown blob with a white cap. The brown is poop, the white is urates, or the equivalent of urine. Everything, including the egg, comes out of the same opening.
But if some starts getting stuck to the feathers, it can build up, and can eventually cause a blockage so the chicken can't poop. And if that happens ... yeah, the chicken can die. I don't know if that's what happened to your hen. But you do want to keep it from happening to this one if you can.
But if some starts getting stuck to the feathers, it can build up, and can eventually cause a blockage so the chicken can't poop. And if that happens ... yeah, the chicken can die. I don't know if that's what happened to your hen. But you do want to keep it from happening to this one if you can.