My cat has placebo kittens.
We have friends with allergies so our cats are strictly outdoors creatures. Occasionally they breech the back door defences and invade the house seeking out hiding places to latch themselves onto like barnacles with claws. Most of the time we are able to remove them before they urinate on something or contaminate all the uncovered food items on the counter. Sometimes we look right past them if they stealthily hide in the middle of the room or on top of a chair - just below eye level, not where cats ought to be hiding. No matter how many times we throw them out, they just keep coming back.
One of our cats is a dainty little black female. She is very friendly, especially for a feline, but far too intelligent for a creature of her size.
We give special attention to pregnant animals. She must know this. For the past several months she has taken to eating enough to get her belly bloated and sitting by the back door mewing incessantly till someone takes notice of her. We let her in, recalling how there was a strange neighborhood cat in the yard a few weeks ago and thinking maybe they got frisky and we'll have kittens in another few weeks. She settles quickly into the luxuries of the indoor life, gloating at the cats outside, lording it over them - her new found position. All is well until the third day when she contaminates the bag of potatoes on the pantry floor and the fat suit is gone. She is thrown out with the other cats and dogs and we promise ourselves that we'll never to fall for that trick again.

Two weeks latter its raining and there she is, mewing at the door, bulging around the belly. A few days later, there's a distinct odor wafting through the kitchen from the pantry. Never again.

Well, here we are again - not willing to risk banishing a pregnant creature - willing to accept the possibility of placebo kittens in our potatoes.