An escape route refers to a path or way to get away from a dangerous or difficult situation. It's like a plan to leave when things get bad or when you need to find safety. Full definition
It's a good idea to provide escape routes for cats such as tall cat trees or rooms inaccessible to dogs. (pethelpful.com)
Make sure that your cat has multiple escape routes from the box, and that it is difficult for another pet or person to sneak up on her while she's in the box. (cat-lovers-only.com)
They like to be able to see people or other animals approaching, and they like to have multiple escape routes in case they want to leave their boxes quickly. (aspca.org)