Foxes have a liking for shoe-stealing, one in Berlin pinched over a 100.
https://www.livescience.com/fox-steals-100-shoes.html
Mrs K. couldn't understand what happened to one of her garden clogs, gave up searching, bought a new pair & the same thing happened, we found one later by the river, she has to bring them indoors at night. It's a common occurrence, no one knows why, it was mooted that it might be something to do with leather, but I recently found one chewed up trainer, also on the riverbank, containing no leather at all.
Re. foxes in the house; will a fox not fit through a cat-flap?