The tabby might have been leaving you a gift. Cats like to share part of the prey with their humans. Just be glad she didn't leave the rat livers on your pillow.
Cats possess a natural instinct to hunt prey, as well as share their catch with loved ones, which can result in a "gift" of a dead animal for owners.
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Cats are born to hunt. Even if domesticated cats know they don’t need to catch their own food to survive, they cannot resist the urge and often enjoy the hunt and chase. Some cats that catch prey will bring their owners the dead animals—or, perhaps even more unpleasantly, sometimes ones that are still alive—to show off their prized catch for later consumption, as a teaching aid, or as a gift.
Additionally, cats are pack animals, and they often want to share their bounty with their family. This is especially true of female cats who would normally teach their young how to hunt and eat. This means when a cat brings you an animal they caught, be it alive or dead, they consider you a part of their family. Their instincts are telling them this is what they need to do to survive and that they need to pass these important, life-saving skills onto their family.
This prey-catching behavior has nothing to do with being hungry. Rather, the “prey” being caught by indoor cats often isn’t edible at all, but rather toy mice, balls, and garbage they felt that they “hunted.” These items may also be presented to you as gifts, even though they are inedible.