I love living in lion country and have had them as pets. Teaches you to maintain awareness of your surroundings.
For 12 years I owned a house on the ridge west of Boulder Creek in the Santa Cruz Mountains. It is common for neighbors there to report seeing cougars, and every once in a while a pet gets attacked.
I now own a house in a more remote area of the Washington Cascades. A large cougar has been trying to get into the fortress I call a poultry coup. The wire is all beat up, but he couldn't get in. It's fun watching him try, although it sure freaks out the chickens.
A bear probably could do it, but they are even more shy around here than the cougars.