There's some places in Tennessee they could exist and never bee seen. The Cumberland Plateau is one place and several large Wild Life Management Areas and a National Recreation Area. Up on the Tn/KY line they could easily exist and not be seen. Especially around the abandoned strip mines. Cherokee National Forest on the TN/NC line would be a possibility as well. In these areas some it doesn't see mans footprint but maybe once a decade. WMA's and National Forest prohibit running of dogs so it would be ideal.
When Yotes first came into the area you didn't see or hear them either. Now they are seen in cities unfortunately. I chased one in Oak Ridge, Tennessee a couple years ago on a highway close to the weapons plants. It was in front of me on a wall divided four lane hold between 25-30 MPH then jumped the wall into the other lane. The jump was too high for a dog especially running full speed. LOL.
That said I've only seen three Bobcats in my life. One was running in front of my headlights on a road close to where I live. It was the longest I got to see one.
I've also heard a tree full of young hoot Owls sound more like a tree full of monkeys yelling. I called then into a campground that was empty except for my family. Saturday night it was full and the kids said call up the owls. I told them it's too much noise going on but I went to a field a couple hundred feet away and called. The darn things lighted in the trees in the campground. It was hilarious. People were yelling What is that LOL.
You’ll see a hundred black bears before you will see a cougar.