Cats

I'm not sure exactly what is going on here. I had to move a litter box to the living room earlier this year because someone, I am not sure who, was pooping in front of the door to the side room. I now have the litter box there, and clean it every day. Honestly.
The last few days I have had to come in through the back door, because someone, I am not sure who, is pooping in front of the front door, so that it gets smooshed into the carpet as I open the door. This is not good. This is stinky. This is a carpet that is going to come up anyhow, and I am tempted to just cut this section out and burn it. What causes them to do this?
I am a little bit aggravated. I think I will go to some yard sales.