Did you ever encounter a runaway predator?
Never. I live in the suburbs of Atlanta Georgia currently so I barely ever see any interesting wildlife at all. I have however been to the Okefenokee swamp and seen black bears, cougars, alligators, and turkeys. Around Georgia I have only seen raccoons, a fox, a and bobcat. Although I have had a dangerous encounter with a coyote, it was trying to intimidate me by snarling and lunging, however its tail was between its legs so it wasn't too confident it could take me. And New York has no interesting wildlife.
No thankfully, however, I have a friend whose son was homeless for a period of time and was trekking through the Oregon forest and had to find a place to sleep because the sun was going down. That same night a lion from a local zoo had escaped and was found in that same forest her son was sleeping but the next morning! Crazy huh?! He was fine btw! Never ran into it and I'm sure that was the last time he slept in a forest!