I once brought a 5-gallon pail of food waste home from a community dinner. I was going to dispose of it, but let it set in the old (100years) garage for a few days. When I found it, there were about 5 mice in it, and they had all drowned. I don't let mice free.
We have cats and a cat door into the breezeway. Our male cat often brought in birds, some not dead yet, and there were feathers all over the place.
And once, when we were away on a trip, the female cat brought a full sized rabbit through that door. The rabbit was not dead yet either. So the cat played with it for quite a while. I mean: blood and guts all over everything. Even half way up the walls. The lady who lives upstairs takes care of our house when we are away and she found the mess. She cleaned up as much as she could, but this was December, and it was cold out there. I felt so sorry for her. I still feel bad about that. Later I had the carpet cleaned by professional cleaners, and they said the blood was no problem. They got it all up.
But a while before that happened, we forgot about a bag of milk out there, and the cats got into that. The cleaners had a much harder time with that. It took several years of cleaning to get rid of that. (I usually get that carpet cleaned once a year.)
I can't imagine having a cat door that would let the cat come directly into the house, but I know some people have them.