do other peoples cat bring in 'pets' thaen get bored with them & let them go,we've had a moose loose for weeks ,mainly under fridge,when all is quiet there are odd noises,which in the wee small hours is creepy
A Little Nipper trap, baited and poked to the back of the fridge with a piece of dowel or similar (gives you the reach without the trap getting your fingers...) will sort the moose.
Don't leave it feasting and weeing in your house, no sentiment where diseases are concerned.