Are there any animal-eating plants?

Yes, although they do not eat anything larger than insects (which, of course, are members of the animal kingdom).
These carnivorous plants capture plants their prey using various means. The pitcher plant has tubelike leaves that hold water, and insects crawl down in to these leaves only to be caught on tiny hairs which line the tube. They then slide down the tube into the water, where eventually they drown.
The sundew has circular leaves, this time covered with hairs on the outside. Each hair has a drop of sticky liquid at its tip which holds on to the insect and prevents its escape, while the leaf curls inwards and traps it, ready for eating
But perhaps the most well-known animal-eating plant is the aptly-named Venus’ fly-trap. This has hinged leaves, again with hairs over their surface When an insect lands on one of these especially sensitive hairs, the leaf closes up on its hinges, trapping the insect inside.