My previous cat in his extreme old age allowed a young stray, also male, to come in and eat the left-overs from his dinner, and sleep behind my husband's wood lathe, or on the indoor wood pile in cold weather.
I was amazed, but I honestly do not think that even at 17 and when he himself may have realised that he did not have much longer to live that he would have allowed any other kind of animal than a cat in.
Might these scraps of skin and fur be a present from your unseen dinner guest?
A cat that hunts is capable of dealing with a weasel or ferret.
Now after the death of my old cat, when I succumbed to temptation and came home with two kittens, we installed the kind of cat flap that is programmed to read our cats' chips and not allow others in.
What the makers do not say is, that if the flap is open so your cats can go out, any cat or suitably sized critter that comes in to your house can get out, as I found out when a newly nubile queenie cat got out that way. (Don't worry, I found her before the neighbourhood's uneutered toms did. She was standing outside, looking sadly at the cat-flap that refused to open for her.)
They also do not tell you, that if your cats are like Topsy and "just grewed" they will decide it is easier to get you to open the back door than to squeeze out through the cat flap, although mine do come in again using their door, rather than mine, quite happily.
I said we should have ordered a dog flap, but do you think DH listened? Our cats are large cats, always, however small they are at 11 weeks.