Here are some great hanging plants that are safe for cats:

1. Donkey’s Tail (Sedum morganianum)
2. Christmas Cactus (Genus Schlumbergera)
3. Lipstick plant (Genus Aeschynanthus)
4. Lace Flower Vine (Alsobia dianthiflora)
5. Hoya carnosa
6. Asparagus Fern (Asparagus densiflorus cv sprengeri)
7. Goldfish Plant (Genus Columnea)

I’d just like to add that any plant can make an animal sick if they eat too much of it. Also, Aeschynanthus, Alsobia, and Columnea are all gesneriads, so it’s likely that most other gesneriads are also safe. I know that African violets, and Genus Episcia are safe for cats, and they’re also gesneriads, but not hanging ones.