She has brought us 'gifts' from time to time; some of them live. She managed to get two live chipmunks in the house, a few birds and a cicada. Once in a while, if I am eating ham and cheese, she will eat small pieces of ham.
No. My big cat would never bring me a dead mouse (or anything else, for that matter). He says that kind of thing is beneath the dignity of a mini panther. If I want a dead mouse (or anything else), I am to go set it myself (and to bring him some cat teats while I'm at it). The only "human" food he'll eat is tuna fish (no matter what it's in).
My little cat encourages me to eat junk food (and to share). This stone deaf cat can "hear" me even thinking about junk food, and will quickly jump into my lap to beg (his begging would put a dog to shame). When I'm finished, he'll clean up any crumbs better than a dog. Yes, to him ANY human food is junk food.
We have two cats. They do not bring their catch to us. Instead, they bring in live things. Chipmunks, frogs, mice, skinks. They brought In a live snake one night, this got them grounded. Locked in the house for a week. The cat door is now locked when we go to bed at night as well.