Cockroach Hotel: The Continuing Story

We still have very big cockroaches at our house. We don't see as many as we used to, only about 4 or 5 a week now. I no longer scream for Gavin to kill them. I do that myself. All in all, I feel that for the most part I handle the situation quite well. There is only one thing that still disturbs me about them, when I wake up in the morning to find half of a cockroach (usually the tail end though not always) where there was no cockroach when I went to bed. What the heck happens to the other half?